Question

A parachutist descending at a speed of 15.1 m/s loses a shoe at an altitude of 41.2 m. What is the speed of the shoe just before it hits the ground? The acceleration due to gravity is 9.81 m/s^2. When does the shoe reach the ground? Answer in units of s.

Answer 1

Answer:

Speed = 32.19 m/s

Time = 1.742 seconds

Explanation:

Given;

Initial speed of the shoe i.e the speed of the parachutist = 15.1 m/s

height above the ground = 41.2 m

Acceleration due to gravity = 9.81 m/s²

Now,

from the Newton's equation of motion

we have

v² - u² = 2as

where,

v is the final speed

u is the initial speed

a is the acceleration = 9.81 m/s²   (since it is a case of free fall )

s is the distance

thus,

we have

v² - 15.1² = 2 × 9.81 × 41.2

or

v² = 808.344 + 228.01

or

v² = 1036.354

or

v = 32.19 m/s

hence,

the speed of shoe just before it hits the ground is 32.19 m/s

also,

from Newton's equation of motion

v = u + at

where, t is the time

thus,

32.19 = 15.1 + 9.81 × t

or

9.81 × t = 17.09

or

t = 1.742 seconds