Projectile motion tennis ball problem

In summary: Distance = 30m/s * 2s = 60m. In summary, the tennis ball will remain in the air for 2 seconds and travel horizontally for a distance of 60 meters when hit with a vertical speed of 10 m/s and a horizontal speed of 30 m/s. The maximum distance can be achieved at any angle, but the angle that will give the maximum distance is 45 degrees.
  • #1
mxer101
3
0

Homework Statement


Tennis Ball hit at a vertical speed of 10 m/s & Horizontal speed of 30 m/s. How long will the ball remain in the air? How far will the ball travel horizontally?


Homework Equations


I am not sure which equation to use? The angle that the ball was hit is not given, would I try all angles? 30,37,45,57,60? I know that 45 would give the max distance


The Attempt at a Solution


Answers given:
How far: 60m
How long: 2s

Thanks!
 
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  • #2
To find how long the ball is in the air, use the equation:

d = v1*t + (1/2)at^2. apply this equation for vertical displacement...
 
  • #3
As vertical and horizontal components of velocities are given, angle is not required. At the highest point the velocity will be zero (v = 0). Initial vertical velocity = u = 10 m/s. Acceleration a = - 9.8 m/s^2 (-ve because acceleration due to gravity is always downwards i.e. opposite of the +ve upwards displacement) Apply v = u + at to get t, the time to reach the highest point. Double that to get the time during which the ball is in air (T).

As the horizontal velocity remains constant throughout, determine horizontal displacement in time T (calculated above) using s = ut
 

1. What is projectile motion in tennis ball problem?

Projectile motion refers to the curved path that a tennis ball follows when thrown or hit. It is caused by the combination of the ball's initial velocity, gravity, and air resistance.

2. How do you calculate the trajectory of a tennis ball?

The trajectory of a tennis ball can be calculated using equations of motion, taking into account the initial velocity, angle of release, and gravitational acceleration. Factors such as air resistance and spin can also affect the trajectory.

3. How does the height and angle of release affect the distance a tennis ball travels?

The height and angle of release can greatly impact the distance a tennis ball travels. A higher height of release and a lower angle of release will result in a longer distance traveled due to the ball having a longer time in the air and a flatter trajectory. On the other hand, a lower height of release and a higher angle of release will result in a shorter distance traveled.

4. Does air resistance affect the trajectory of a tennis ball?

Yes, air resistance does affect the trajectory of a tennis ball. The more surface area the ball has, the more air resistance it will experience, causing it to slow down and have a shorter distance traveled. This is why tennis balls with less air resistance, such as those used on clay courts, tend to travel faster and farther.

5. How does spin affect the trajectory of a tennis ball?

Spin can greatly affect the trajectory of a tennis ball. Topspin, where the ball rotates forward, can cause the ball to dip earlier and bounce higher, while backspin, where the ball rotates backward, can cause the ball to float and bounce lower. Sidespin can also cause the ball to curve in a certain direction, making it more difficult for the opponent to return.

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