Posted by **Kristina** on Thursday, December 18, 2008 at 9:06pm.

This is a projectile motion problem where I need to find the velocity and angle I launch a ball at to hit a ship. The ball is on a cliff 400 m high, and the ship is 250 m away from the cliff. The ship is moving away at a velocity of 40 m/s. What velocity and angle should I launch the ball at so it hits the ship? And how do i solve this? Thank you.

- Physics -
**bobpursley**, Thursday, December 18, 2008 at 9:21pm
The ship is moving at 40m/second? I don't believe it. That is over 80miles/hour.

You have to aim at where the ship will be.

let it be 250+x

but x=40*timeinair

now time in air is found from....

1) hf=hi+ViSinTheta*time-1/2 g time^2

Notice that is a quadratic.

and the horizontal equation..

250+x=Vicostheta*time

2)250+40*time=ViCostheta*time

So you have two equations, two unknowns. Which means you can choose an arbritary value for one. Theta is the most complicated, so choose a launch angle. Lets make Theta 32 deg.

Find the cos32, sin32 and put those in the equation.

Now in the second equation, solve for Vi in terms of time. Now put that value of Vi in the first equation, and solve for time. You have it all.

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