A tennis player aims to serve the ball horizontally when their racquet is 2.5 m above the ground. The distance from the player to the net is 15.0 m and the net is 0.9 m high

(a) What is the minimum speed with which the ball must leave the racquet if it is to just clear the net?
(b) How far beyond the net does the ball land?
(c) If the distance from the net to the service line is 7.0 m is the ball “in” or “out’?
(d) What is the total time for which the ball is in the air from the time that it leaves the racquet until it hits the ground?

delta(y)=(1/2)*g*t^2

solve for t.
1.6=4.9t^2
t=.57143

delta(x)=Vo*t
solve for Vo.
15=Vo*.57143
Vo=26.25m/s

19.2 m/s

To solve these problems, we can use the principles of projectile motion. Let's break it down and solve each part step by step:

(a) To find the minimum speed with which the ball must leave the racquet to clear the net, we need to consider the horizontal and vertical components of the motion separately.

The net is 0.9 m high, so the ball must cross this height while traveling a horizontal distance of 15.0 m. We can use the equation of motion for vertical motion:

Δy = v₀y * t + (1/2) * a * t²

Since the ball starts and lands at the same height, the vertical displacement (Δy) is zero. Therefore, we have:

0 = v₀y * t - (1/2) * g * t²

where v₀y is the initial velocity in the vertical direction, t is the time of flight, and g is the acceleration due to gravity (-9.8 m/s²).

Solving this equation for v₀y, we get:

v₀y = (1/2) * g * t

The horizontal distance covered by the ball is 15.0 m, and the time of flight t is the same for both horizontal and vertical motion. So we can use:

Δx = v₀x * t

where Δx is the horizontal distance covered, and v₀x is the initial velocity in the horizontal direction.

Since the ball is aimed horizontally, the initial velocity in the vertical direction (v₀y) is zero. Therefore, the initial velocity in the horizontal direction (v₀x) is the same as the overall speed of the ball.

Combining the two equations, we have:

v₀x = Δx / t

Substituting the values given, Δx = 15.0 m, and t is the time found from the vertical equation, we can calculate v₀x.

(b) To find how far beyond the net the ball lands, we need to determine the horizontal distance covered by the ball. We already know that the horizontal distance covered is 15.0 m, but this is the distance from the player to the net. To find the distance beyond the net, we need to subtract the width of the net.

(c) To determine if the ball is "in" or "out," we need to check if it lands within the service line, which is 7.0 m from the net. If the horizontal distance covered by the ball (found in part b) is less than or equal to 7.0 m, then the ball is "in." Otherwise, it is "out."

(d) To find the total time for which the ball is in the air, we can use the time of flight (t) obtained from part a.

Now, let's apply these steps to calculate each part of the problem.

7.69 m/s