Projectile Cruves problem

**Paymemoney** · October 23rd 2010, 12:34 AM

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

**skeeter** · October 23rd 2010, 02:57 AM

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

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

**Soroban** · October 23rd 2010, 05:02 AM

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: . $x \:=\:30t$

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

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

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

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

**Paymemoney** · October 23rd 2010, 02:00 PM

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

**skeeter** · October 23rd 2010, 03:29 PM

Originally Posted by Paymemoney

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

no, it would not.

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