A helicopter lifts a 72kg astronaut 15m vertically from the ocean… - Vidyadip

Question

A helicopter lifts a $72kg$ astronaut $15m$ vertically from the ocean by means of a cable. The acceleration of the astronaut is $\frac{\text{g}}{10}$.

How much work is done on the astronaut by:

The force from the helicopter and
The gravitational force on him?
What are the kinetic energy and
The speed of the astronaut just before he reaches the helicopter?(Take, $g = 10ms^{‑2}$)

✓

Answer

Here, mass of astronaut m = 72kg, vertical distance
h = 15m and acceleration of astronaut $\text{a}=\frac{\text{g}}{10}$

Force ftom the helicopte

$\text{F}=\text{mg}+\text{ma}$
$=\text{mg}+\frac{\text{mg}}{10}=\frac{11\text{mg}}{10}$
$\therefore$ Work done by force from the helicopter
$\text{W}=\text{F}\times\text{h}=\frac{11\text{mg}}{10}\times\text{h}$
$\text{W}=\frac{11\times72\times10\times15}{10}$
$=11880\text{J}$

Work done by gavitational force

$\text{W}'=\text{(mg)}(\text{h})(\cos180^\circ)$
$\text{W}'=-\text{mgh}=-72\times10\times15$
$=-10800\text{J}$

KE of astronaut K = network done on him

= W + W'
= (11880 - 10800)J
= +1080J

As $\text{KE}=\frac{1}{2}\text{mv}^2$, Hence

$\text{v}=\sqrt{\frac{2\text{K}}{\text{m}}}$
$=\sqrt{\frac{2\times1080}{72}}$
$=5.48\text{ms}^{-1}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Work, Energy, and Power→Work, Energy, and Power — all question types→Physics STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

An object starts from rest and covers a total distance X in the following manner: It first has a uniform acceleration $a_1$ for some time $t_1$, moves with the speed acquired at the end of $t_1$ for some distance and is then given a uniform retardation $a_2$ so that it is again at rest at the end of the journey. Show that the journey is covered in least time if the body is accelerated for a time of $\Big[\frac{2\text{X a}_2}{\text{a}_1(\text{a}_1+\text{a}_2)}\Big]^{\frac{1}{2}}$ and this minimum time is $\Bigg[2\text{X}\Big(\frac{1}{\text{a}_1}+\frac{1}{\text{a}_2}\Big)\Bigg]^{\frac{1}{2}}.$

Write Newton's law of cooling and state its necessary conditions. Derivation of Newton's law of cooling from Stefan's law.

Consider the situation shown in figure. The elevator is going up with an acceleration of $2.00m/s^2$ and the focal length of the mirror is 12.0cm. All the surfaces are smooth and the pulley is light. The mass-pulley system is released from rest (with respect to the elevator) at t = 0 when the distance of B from the mirror is $42.0cm$. Find the distance between the image of the block B and the mirror at $t = 0.200s$. Take $g = 10m/s^2$.

In the HCl molecule, the separation between the nuclei of the two atoms is about $1.27\mathring{\text{A}}\big(1\mathring{\text{A}}= 10^{-10} \text{m}\big).$ Find the approximate location of the CM of the molecule, given that a chlorine atom is about 35.5 times as massive as a hydrogen atom and nearly all the mass of an atom is concentrated in its nucleus.

A bullet of mass $20g$ travelling horizontally with a speed of $500m/s$ passes through a wooden block of mass $10.0kg$ initially at rest on a level surface. The bullet emerges with a speed of $100m/s$ and the block slides $20cm$ on the surface before coming to rest. Find the friction coefficient between the block and the surface.

A metre stick is balanced on a knife edge at its centre. When two coins, each of mass 5g are put one on top of the other at the 12.0cm mark, the stick is found to be balanced at 45.0cm. What is the mass of the metre stick?

If a drop of liquid breaks into smaller droplets, it results in lowering of temperature of the droplets. Let a drop of radius R, break into N small droplets each of radius r. Estimate the drop in temperature.

Two tuning forks A and B give 5 beats/sec. A resounds with a closed column of air 15cm long and B with an open column 30.5cm long. Calculate their frequencies (neglect end correction).

Consider the de Broglie wavelength of an electron and a proton. Which wavelength is smaller if the two particles have.

The same speed.
The same momentum.
The same energy?.

A satellite of mass $1000kg$ is supposed to orbit the earth at a height of $2000km$ above the earth's surface. Find

Its speed in the orbit.
Its kinetic energy.
The potential energy of the earth-satellite system.
Its time period. Mass of the earth = $6 \times 10^{24}kg$.