In how many seconds will the projectile strike the ground?

Question

A projectile is fired with an initial velocity of 500 feet per second at an angle of 45° with the horizontal. In how
many seconds will the projectile strike the ground? (Round your answer to the nearest tenth of a second.) The
parametric equations for the path of the projectile are:

x = (500 cos 45°)t, and
y = (500 sin 45°)t - 16t2.

 

What formula would you use?

Answer 1

Set y = 0 and solve the resulting quadratic equation for t.

 

0 = -16t² + (500sin45°)t = t(-16t + 500sin45°) 

 

There are 2 solutions:

 

(1)

 

t = 0, but that is when you start from the ground, so ignore this one.

 

(2)

 

-16t + 500sin45° = 0

 

Solve for t, which you can do easily.  This is the solution you want.