Question

A physics book was thrown from the top of a library with a speed of 8.0 m/s at angle 60o with the horizontal. After 5 seconds, the book hits the ground:

(a) Find the height of the library above the ground.
(b) Find the distance of the point where the book falls on the ground from the base of the library.

(c) Just before the book hits the ground, find the horizontal and vertical components of its velocity.

Answer 1

Given the initial speed of the book is u = 8m/s and the angle of projection . The total time taken by the book to reach the ground is 5s. The path of the book is shown in the diagram below.

(a) The time taken by the projectile to reach the ground is the time taken to travelfrom A to B and then B to C. The time taken by the projectile to travel from A to B is the time of flight of the projectile. It is given by,

So the time taken to travel from B to C is,

So the height of the building h is given by,

So the height of the library above the ground is 88.02m

(b) The distance of the point where the book falls on the ground from the base of the library is the sum of the range of the projectile and the horizontal distance travelled by the book from B to C using the velocity . The range of the projectile is given by,

The horizontal distance travelled by the book from B to C is given by,

Now the total distance is,

So h the distance of the point where the book falls on the ground from the base of the library is 20.01m.

(c) The horizontal component of its velocity just before the book hits the ground is,

The vertical component of its velocity just before the book hits the ground is,

So the horizontal and vertical components of its velocity just before the book hits the ground is 4ms and 42.11 m/s respectively.