# Calculus Problems Acceleration

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**Calculus; Displacement, Velocity, Acceleration problem.?**

A coin is dropped from the top of a building 150m high. using a = -9.8 m/s^2.

a. How long will it take for the coin to strike the ground?

b. With what velocity will the coin strike the ground?

This should be pretty simple. I tried it myself. But I got irrational numbers as answers. If that’s OK with you, follow this answer.

NOTE: 150/4.9, its square root and square root of 2940 are all listed as approximate values.

u = 0

h = 150

g = 9.8 m/s^2 (You must take it to be positive as acceleration is in the direction of motion, that is downward)

h = ut + (gt^2)/2

h = 0 + 4.9t^2

4.9t^2 = 150

t^2 = 150/4.9

t^2 = 30.58

t = 5.53

Time taken to strike ground is approximately 5.53 seconds

v^2 – u^2 = 2gh

v^2 = 19.6*150

v^2 = 2940

v = 54.22

The coin hits the ground at approximately 54.22 m/s

**Classic AP Calculus Free Response Problem**