# Thread: Projectile Cruves problem

1. ## Projectile Cruves problem

Hi
The following question i am having problem with:
A tennis ball is served horizontally from 2.5m above the ground at 30m/sec. The net is 12m away and 0.9m high.
a) Find its velocity (v) at any time t seconds

This is what i done:

a=-gj

find the integral to get velocity

v=c_1 i + (-gt+c_2)j

v=12.6i+(-9.8t+2.5)j

P.S

2. the position and height of the net have nothing to do with the ball's velocity unless the ball hits it.

v(t) = 30i - (gt)j

$\displaystyle 0 \le t < \sqrt{\frac{5}{g}}$

3. Hello, Paymemoney!

A tennis ball is served horizontally from 2.5 m above the ground at 30 m/sec.

a) Find its velocity (v) at any time t seconds.

This is a Projectile problem; there is vertical and horizontal displacement.

The horizontal position is: .$\displaystyle x \:=\:30t$

The vertical position is: .$\displaystyle y \:=\:2.5 - 4.9t^2$

The velocity is a vector; it has magnitude and direction.

. . The magnitude is: .$\displaystyle |\vec v| \;=\;\sqrt{\left(\frac{dx}{dt}\right)^2 + \left(\frac{dy}{dt}\right)^2}$

. . The direction is: .$\displaystyle \theta \;=\;\tan^{-1}\left(\dfrac{\frac{dy}{dt}}{\frac{dx}{dt}}\right )$

4. So the velocity would be $\displaystyle 30-\sqrt{9.8t}$

5. Originally Posted by Paymemoney
So the velocity would be $\displaystyle 30-\sqrt{9.8t}$
no, it would not.