h(t)=-16t^2+32t+128

Question

The height of a projectile launched upward at a speed of 32 feet/second from a height of 128 feet is given by the function h(t)=-16t^2+32t+128. How long will it take the projectile to hit the ground?

Answer 1

Hi Jennie,

In this case, the key to understanding how to solve this problem is to realize that when the projectile "hits the ground," the height is going to be 0. This is our GIVEN information and what are trying to find is the t, the time when that happens.

So in other words, given this equation: h(t)=-16t²+32t+128, we want to set the equation equal to 0 and solve for t.

0 = -16t²+32t+128

You can do this by:

1) Graphing

2) The Quadratic Formula

3) Factoring

In many cases with this type of equation, the answer ends up being not an integer, so graphing or using the quadratic formula is usually the best way to go. However, in this case, this equation does factor quite nicely, so I'll show you how to solve it by factoring.

Step 0 (Given Equation): 0 = -16t²+32t+128

Step 1 (Factor out the greatest common factor, -16): 0 = -16(t² - 2t - 8)

Step 2 (Factor the trinomial inside the parentheses): 0 = -16 (t - 4)(t + 2)

Step 3 (Set each factor equal to 0 and solve for t)

t - 4 = 0 --> t = 4

t + 2 = 0 --> t = -2

Step 4 (Re-read the problem and decide which answer makes more sense in the given context):

Given that "t" represents the time after the projectile was launched, it doesn't make sense for it to be negative... so the only possible answer is t = 4.

So the projectile hits the ground after 4 seconds.

Hope this was helpful! Feel free to reach out to schedule one-on-one lessons for more support :)

Answer 2

0 = -16t² + 32t + 128

Can you solve for t and answer?