This is not something that is obvious but if you think about the ball that drops straight down gets pulled down by gravity and the ball that is thrown straight out gets pulled down by gravity as well. As gravity is the only force in both cases, both balls will hit the ground at the same time.
When you throw a ball, we are assuming that you are throwing it horizontally. This means you are giving the ball only horizontal velocity. The correct answer is the last one: the two will hit the ground at the exact same time.
This is because gravity accelerates all objects equally, even if one object is heavier than the other. The watermelon also has a lower acceleration because it is heavier and the egg the opposite.
Many beginning road cyclists ride at average speeds between 10 and 14 mph on the road. It can definitely be achieved with a decent hill on a road but is tough to obtain purely on flat. Below is a Strava speed graph from one of my MTB rides and a ride on a commuter path.
From then on, the stone behaves exactly like a stone throw downward with the same initial speed. Galileo experimented with balls rolling down inclined planes, in order to reduce the acceleration along the plane and thus reduce the rate of descent of the balls. A pebble is dropped into a water well, and the splash is heard 16 s later.
What is the approximate distance from the rim of the well to the water's surface? A hard rubber ball, released at chest height, falls to the pavement and bounces back to nearly the same height. When it is in contact with the pavement, the lower side of the ball is temporarily flattened.
Assume that the maximum depth of the dent in the ball is about 1 cm. On level ground, we define range to be the horizontal distance traveled by a projectile. Galileo and many others were interested in the range of projectiles primarily for military purposes—such as aiming cannons. However, investigating the range of projectiles can shed light on other interesting phenomena, such as the orbits of satellites around the Earth.
Let us consider projectile range further. How does the initial velocity of a projectile affect its range? Obviously, the greater the initial speed , the greater the range, as shown in Figure a. The initial angle also has a dramatic effect on the range, as illustrated in Figure b. For a fixed initial speed, such as might be produced by a cannon, the maximum range is obtained with. This is true only for conditions neglecting air resistance. If air resistance is considered, the maximum angle is approximately.
Interestingly, for every initial angle except , there are two angles that give the same range—the sum of those angles is. The range also depends on the value of the acceleration of gravity.
The lunar astronaut Alan Shepherd was able to drive a golf ball a great distance on the Moon because gravity is weaker there. The range of a projectile on level ground for which air resistance is negligible is given by. The proof of this equation is left as an end-of-chapter problem hints are given , but it does fit the major features of projectile range as described.
When we speak of the range of a projectile on level ground, we assume that is very small compared with the circumference of the Earth. If, however, the range is large, the Earth curves away below the projectile and acceleration of gravity changes direction along the path. The range is larger than predicted by the range equation given above because the projectile has farther to fall than it would on level ground. If the initial speed is great enough, the projectile goes into orbit.
This possibility was recognized centuries before it could be accomplished. When an object is in orbit, the Earth curves away from underneath the object at the same rate as it falls.
The object thus falls continuously but never hits the surface. These and other aspects of orbital motion, such as the rotation of the Earth, will be covered analytically and in greater depth later in this text.
Once again we see that thinking about one topic, such as the range of a projectile, can lead us to others, such as the Earth orbits. In Addition of Velocities , we will examine the addition of velocities, which is another important aspect of two-dimensional kinematics and will also yield insights beyond the immediate topic. Learn about projectile motion by firing various objects.
Set the angle, initial speed, and mass. Add air resistance. Make a game out of this simulation by trying to hit a target. Answer the following questions for projectile motion on level ground assuming negligible air resistance the initial angle being neither nor : a Is the velocity ever zero?
A maximum? Answer the following questions for projectile motion on level ground assuming negligible air resistance the initial angle being neither nor : a Is the acceleration ever zero? For a fixed initial speed, the range of a projectile is determined by the angle at which it is fired. For all but the maximum, there are two angles that give the same range. Considering factors that might affect the ability of an archer to hit a target, such as wind, explain why the smaller angle closer to the horizontal is preferable.
When would it be necessary for the archer to use the larger angle? Why does the punter in a football game use the higher trajectory? During a lecture demonstration, a professor places two coins on the edge of a table. She then flicks one of the coins horizontally off the table, simultaneously nudging the other over the edge. Describe the subsequent motion of the two coins, in particular discussing whether they hit the floor at the same time. A projectile is launched at ground level with an initial speed of It strikes a target above the ground 3.
What are the and distances from where the projectile was launched to where it lands? A ball is thrown horizontally from the top of a Ignore air resistance. How many buses can he clear if the top of the takeoff ramp is at the same height as the bus tops and the buses are Neglect air resistance.
An archer shoots an arrow at a In this part of the problem, explicitly show how you follow the steps involved in solving projectile motion problems. Will the arrow go over or under the branch?
A rugby player passes the ball 7. Verify the ranges for the projectiles in Figure a for and the given initial velocities. The cannon on a battleship can fire a shell a maximum distance of Assume that the radius of the Earth is.
How many meters lower will its surface be Does your answer imply that error introduced by the assumption of a flat Earth in projectile motion is significant here? An arrow is shot from a height of 1. It lands on the top edge of the cliff 4. In the standing broad jump, one squats and then pushes off with the legs to see how far one can jump.
Suppose the extension of the legs from the crouch position is 0. The speeds remember, speed is the magnitude of the isntantaneous velocity, although this isn't a big issue in this problem are going to be exactly the same. Although the ball you throw downward will get to the ground sooner, the final velocity and speed of each ball will be exactly the same. In later chapters, you'll have a different way of figuring this out. For now, the thing to do is to set up the problem two different ways: one with an initial velocity that is positive, and the other with an initial velocity same magnitude that is negative.
Then solve for the final velocity. You'll find that they're exactly the same. Another way to think about it: The ball that you throw straight up is going to accelerate just as much when it's traveling upwards as when it travels downward -- always accelerating at the rate of g.
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