Question

A bullet is shot upwards and its trajectory can be modeled by the function h(t) = -t^4 + 15t^3 - 150t^2 + 1600t + 3000, where h(t) is measured in meters and t is the number of seconds since the bullet is shot. At what second did the bullet hit the ground?

Option 1: 4 seconds
Option 2: 5 seconds
Option 3: 6 seconds
Option 4: 7 seconds

Answer 1

The bullet hits the ground at approximately 5 seconds.

Step-by-step explanation:

The bullet hits the ground when its height, h(t), is equal to zero. We can find the time, t, when this occurs by setting h(t) equal to zero and solving for t. So we have:

0 = -t^4 + 15t^3 - 150t^2 + 1600t + 3000

By using the quadratic formula or using numerical methods, we find that the bullet hits the ground at approximately t = 5 seconds.