Question

An object is thrown from a building 160 feet above the ground with an initial velocity of 48 ft/sec, where t is measured in seconds. If acceleration due to gravity is -16 ft/s^2, find the maximum height of the object. Explain.

Answer 1

To find the maximum height of the object, we can use the equation h = v0*t - 0.5*g*t^2, where h is the maximum height, v0 is the initial velocity, t is the time, and g is the acceleration due to gravity. Substituting the given values, we find that the maximum height is 72 feet.

Step-by-step explanation:

To find the maximum height of the object, we need to determine the time it takes for the object to reach its highest point. Since the object is thrown upwards, the initial velocity will decrease due to acceleration due to gravity. The formula to calculate the time it takes to reach the highest point is given by:

t = v0/g

where t is the time, v0 is the initial velocity, and g is the acceleration due to gravity.

Substituting the given values, we have:

t = 48 ft/sec / 16 ft/s2 = 3 seconds

Now, to find the maximum height, we can use the equation:

h = v0*t - 0.5*g*t2

where h is the maximum height.

Substituting the given values, we have:

h = 48 ft/sec * 3 sec - 0.5 * 16 ft/s2 * (3 sec)2 = 144 ft - 72 ft = 72 ft

Therefore, the maximum height of the object is 72 feet.