# Lesson Worksheet: Vertical Motion under Gravity Mathematics

In this worksheet, we will practice using the kinematics equations of uniform acceleration to model the vertical motion of a body with uniform acceleration due to gravity.

Q1:

A stone was thrown down a well at 2 m/s. It reached the bottom in 1.5 seconds. Determine the depth of the well, given that the acceleration due to gravity 9.8 m/s2.

Q2:

If an apple falls from a tree and takes 1.5 seconds to reach the ground, at what velocity does it hit the ground? Take the acceleration due to gravity .

Q3:

A body was projected vertically upward at 18.3 m/s from a point 163 m above the ground. Find the position of the body 5 seconds after it was projected. Take .

Q4:

Fill in the blank: If a body is projected vertically upward with speed to reach maximum height , then the speed that the body should be projected by to reach height is .

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Q5:

If a body, which was dropped from a building, took 3 seconds to reach the ground, find its average velocity as it fell. Let the acceleration due to gravity .

Q6:

A body was projected vertically downwards from the top of a tower whose height is 80 m. Given that it covered 35.9 m during the 1st second of its motion, find the time taken to reach the ground rounded to the nearest two decimal places. Let the acceleration due to gravity .

Q7:

A particle is projected vertically upward at 7 m/s from a point 38.7 m above the ground. Find the maximum height the particle can reach from the ground. Consider the acceleration due to gravity to be 9.8 m/s2.

Q8:

A particle was projected vertically upward from the ground. Given that the maximum height the particle reached was 62.5 m, find the velocity at which it was projected. Take the acceleration due to gravity .

Q9:

A body fell vertically from the top of a tower. It covered 86.73 m in the final second before hitting the ground. Determine the height of the tower rounding your answer to the nearest two decimal places. Let the acceleration due to gravity .

Q10:

A ball was projected upward from a window. It returned to the window 2.8 seconds after it had been projected. Find the maximum height that the ball reached above the window, given that the acceleration due to gravity is .