Highest point on trajectory of tennis ball

[firebird99]

Homework Statement

A tennis ball is thrown toward a vertical wall with a speed of 21.0 m/s at an angle of 40.0 degrees above the horizontal. The horizontal distance between the wall and the point where the tennis ball is released is 23.0 m.

a. At what height above the point of release does the tennis ball hit the wall?

b. Has the tennis ball already passed the highest point on its trajectory when it hits the wall? Justify your answer.

Homework Equations

The Attempt at a Solution

Sorry i can't provide more information but my teacher assigned us this problem, he said it would be difficult and honestly I have no idea what to do. Any help will be appreciated.

Thank-you

 

[tiny-tim]

Welcome to PF!

Hi firebird99! Welcome to PF!

Use the standard constant acceleration equations for the x and y directions separately, to get two equations for t and h, and then eliminate t.

 

[kerimek]

for sharing this problem. As a scientist, it is important to approach problems systematically and use the available information to make educated conclusions. In this scenario, we have a tennis ball being thrown at a wall with a known initial velocity and angle. We also have the distance between the wall and the release point.

To answer part a of the question, we can use the equation for the height of a projectile, h = h0 + v0y*t - 1/2*g*t^2, where h0 is the initial height, v0y is the initial vertical velocity, g is the gravitational acceleration, and t is the time. We know that at the highest point of the trajectory, the vertical velocity is equal to 0, so we can set v0y = 0 and solve for t. We can then plug in the value of t into the equation to find the height at the highest point.

For part b, we need to consider the motion of the tennis ball. Since it is being thrown at an angle, it follows a parabolic path and reaches its highest point at some point during its trajectory. When it hits the wall, it is still moving downwards, so it has not yet reached its highest point. This can also be seen from the equation for the vertical velocity, v = v0y - g*t, where the velocity is negative when the ball is moving downwards. Therefore, the tennis ball has not yet passed the highest point on its trajectory when it hits the wall.

I hope this helps in your understanding of the problem. It is important to always use the given information and apply relevant equations to solve problems in a systematic and logical manner.