Question

An rock is thrown upward from a platform that is 235 feet above ground at 55 feet per second. Use the projectile formula

h
=
−
16
t
2
+
v
0
t
+
h
0
to determine when the rock hit the ground.

[Recall that
v
0
is the initial velocity of the object and
h
0
is the inital height of the object.]

Answer: The rock will hit the ground after

Select an answer

Answer 1

Answer: The correct answer is approximately 7.32 seconds.

Explanation:

To determine when the rock hits the ground, we can set the height (h) in the projectile formula to 0, as the ground level is the reference point.

The projectile formula is given as:

h = -16t^2 + v0t + h0

Where:

h is the height at time t,

t is the time in seconds,

v0 is the initial velocity,

h0 is the initial height.

In this case, the initial height (h0) is 235 feet, and the initial velocity (v0) is 55 feet per second.

Setting h = 0, we can solve for t:

0 = -16t^2 + 55t + 235

To find when the rock hits the ground, we need to solve this quadratic equation for t.

Using a quadratic formula or factoring, we find that the solutions are approximately t = 7.32 seconds and t = -2.57 seconds.

Since time cannot be negative in this context, we discard the negative value.

Therefore, the rock will hit the ground after approximately 7.32 seconds.