Question

An object is thrown upward from an initial height of 40 feet with an initial velocity of 10 feet per second. Which of the following represents the time it takes for the object to hit the ground?

A) 5 seconds
B) 2 seconds
C) 4 seconds
D) 3 seconds

Answer 1

The time it takes for the object to hit the ground is 3 seconds.

Step-by-step explanation:

The time it takes for the object to hit the ground can be determined using the kinematic equation:

h = h0 + v0t + (1/2)gt2

Where:

• h is the final height of the object (0 feet, as it hits the ground)
• h0 is the initial height (40 feet)
• v0 is the initial velocity (10 feet per second)
• t is the time it takes for the object to hit the ground
• g is the acceleration due to gravity (-32 feet per second squared)

Plugging in the values:

0 = 40 + 10t - 16t2

16t2 - 10t - 40 = 0

Solving this quadratic equation gives two possible values for t: t = 3 seconds and t = -1.25 seconds. Since time cannot be negative, the answer is 3 seconds (D).