Question

A parachutist drops first freely from an airplane for 10s and then his parachute opens out. Now he descends with a net retardation of $2.5m{s^{ - 1}}$ If he bails out of the plane at a height of 2495m and g = $10m{s^{ - 2}}$ his velocity on reaching the ground will be

A.)$5m{s^{ - 1}}$
B.)$10m{s^{ - 1}}$
C.)$15m{s^{ - 1}}$
D.)$20m{s^{ - 1}}$

Answer 1

Hint- It is a problem of kinematics, in which we will use the three equations of the motion, he firstly falls freely where he has acceleration due to gravitation then he opens the parachute and retards with some value finally reaching ground with some value.

Complete step-by-step answer:
Let u be the initial velocity of the parachutist when he jumps from the airplane at t = 0
Let v be the final velocity of the parachutist at time t = 10s.

Let a be the retardation

Given

$u = 0$
$a = 2.5m{s^{ - 2}}$

As we know that

$v = u + at$

Substituting the value of initial velocity and time t = 10s and a = g = 10 for final velocity

\[
  v = 0 + 10 \times 10 \\
  v = 100m{s^{ - 1}} \\
 \]

In order to calculate the distance covered, we will use the formula

$s = ut + \dfrac{1}{2}a{t^2}$

Substituting the value of initial velocity and time t = 10s and a = g = 10 for distance

$
  s = 0 + \dfrac{1}{2} \times 10 \times {10^2} \\
  s = 500m \\
$

As the body retards with retardation $a = 2.5m{s^{ - 2}}$

Now the distance till he reaches the ground = total distance – the distance covered in first 10sec

$
   = 2495 - 500 \\
   = 1995m \\
$

As we know

${v^2} = {u^2} + 2as$

Substituting the value of initial velocity and time t = 10s and a = -2.5 for final velocity

\[
  {v^2} = {100^2} + 2\left( { - 2.5} \right)\left( {1995} \right) \\
  {v^2} = 10000 - 9975 \\
  {v^2} = 25 \\
  v = 5m{s^{ - 1}} \\
\]

Hence, the final velocity of the parachutist is $v = 5m{s^{ - 1}}$ and the correct option is A.

Note- In order to solve these types of questions, remember the basic equations of motions and solve the question step by step. Also frame the equations from the given conditions and number of unknowns must be equal to the number of equations. There are two forces acting on a parachute with a parachutist: the force of gravity and the air resistance. The force of retardation is due to air resistance.