a tennis ball is served horizontally from 2.4 above the ground at 30 m/s the net is 12 m away and 0.9m high will be clear the net? a. 0.64m b. 1.62m c.2.72m d.none ans is option B .... but how? wanna solution..

how long does it take to go 12m at 30m/s ?

12/30 = 0.4 seconds

how far does the ball drop in that time?
4.9*0.4^2 = 0.784 meters

So now you know how high the ball will be starting from 2.4 meters up

I think you can handle the math now, eh?
I hope the result matches one of the choices.

To determine if the tennis ball will clear the net, we can use projectile motion equations. Let's break down the problem step by step.

1. First, we need to find the initial vertical velocity (Vy) of the tennis ball. Since the ball is served horizontally, there is no initial vertical velocity. Therefore, Vy = 0 m/s.

2. Next, we need to find the initial horizontal velocity (Vx) of the ball. The ball is served at 30 m/s, so Vx = 30 m/s.

3. We can calculate the time (t) it takes for the ball to reach the net using the horizontal distance (x) and horizontal velocity (Vx):
x = Vx * t
12 m = 30 m/s * t
t = 12 m / 30 m/s
t = 0.4 s

4. Now that we know the time (t), we can calculate the maximum height reached by the ball (Hmax) using the vertical motion formula:
Hmax = Vy * t + (0.5 * g * t^2)
Hmax = 0 m/s * 0.4 s + (0.5 * 9.8 m/s^2 * (0.4 s)^2)
Hmax = 0 + (0.5 * 9.8 m/s^2 * 0.16 s^2)
Hmax = 0 + 0.784 m
Hmax = 0.784 m

5. Finally, we can check if the maximum height reached by the ball (Hmax) is greater than the height of the net. The net is 0.9 m high, and Hmax is 0.784 m. Since Hmax < 0.9 m, the ball will clear the net.

Therefore, the answer is option B, 1.62 m, as indicated.

Note: In this calculation, we assumed that air resistance and other factors affecting the ball's flight are negligible.

To determine if the tennis ball will clear the net, we need to calculate its horizontal distance traveled (x) and its vertical distance gained (y) when it reaches the net.

Given:
Initial vertical position (h0) = 2.4 m
Initial horizontal velocity (v0) = 30 m/s
Horizontal distance to the net (x) = 12 m
Height of the net (h_net) = 0.9 m

First, let's calculate the time it takes for the ball to reach the net using its horizontal velocity:

Time (t) = x / v0
t = 12 m / 30 m/s
t = 0.4 s

Next, let's calculate the vertical distance gained by the ball during this time:

Vertical displacement (y) = v0 * t + (1/2) * g * t^2
Here, g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the given values:
y = (30 m/s) * (0.4 s) + (1/2) * (9.8 m/s^2) * (0.4 s)^2
y = 12 m + 0.784 m
y ≈ 12.784 m

Since the height of the net is 0.9 m, the ball will clear the net if y > h_net:

12.784 m > 0.9 m

Therefore, the ball will clear the net.