How do you determine the velocity in which the object hits the ground if you use #a(t)= -32# feet per second squared as the acceleration due to gravity and an object is thrown vertically downward from the top of a 480-foot building with an initial velocity of 64 feet per second?

Question

Christopher Agresta · Accepted Answer

Have a look at this:

Isaiah Allen · Answer

undefined To determine the velocity at which the object hits the ground, use the formula for the final velocity of an object in free fall:

$$ v_f = v_i + at $$

Where:
- $ v_f $ is the final velocity
- $ v_i $ is the initial velocity (64 feet per second downward)
- $ a $ is the acceleration due to gravity (-32 feet per second squared, negative because it is downward)
- $ t $ is the time it takes for the object to hit the ground

First, find the time it takes for the object to hit the ground using the formula for the distance fallen in free fall:

$$ d = \frac{1}{2} a t^2 $$

Where:
- $ d $ is the distance fallen (480 feet, the height of the building)
- $ a $ is the acceleration due to gravity (-32 feet per second squared)
- $ t $ is the time it takes to fall

Rearrange the formula to solve for $ t $:

$$ t = \sqrt{\frac{2d}{a}} $$

Substitute the values of $ d $ and $ a $ into the formula and calculate $ t $. Then, substitute the value of $ t $ into the first formula to find the final velocity $ v_f $.