Question

A body of mass 1.5 kg is thrown vertically upwards with an initial velocity of 40 m/s reaches its

highest point after 3 s. The air resistance acting on the body during the ascent is (assuming air

resistance to be uniform, g = 10 m/s2

)

(A) 35 N (B) 25 N (C) 15 N (D) 5 N​

Answer 1

Answer:

The air resistance acting on the body during the ascent is 5 N i.e.option(D).

Explanation:

The time period of motion can be calculated as,

$\mathrm{T=\frac{u}{g+a} }$          (1)

Where,

T=time period of motion

u=initial velocity of the body

g=acceleration due to gravity=10m/s²

a=acceleration produced on the body

From the question we have,

The mass of the body=1.5 kg

The initial velocity with which the body is thrown upwards=40 m/s

The time period of motion(T)=3 seconds

Inserting the values of "T", "u", and "g" in equation (1) we get;

$\mathrm{3=\frac{40}{10+a} }$

$\mathrm{3(10+a)=40}$

$\mathrm{30+3a=40}$

$\mathrm{3a=40-30}$

$\mathrm{3a=10}$

$\mathrm{a=\frac{10}{3}\ m/s^2 }$           (2)

The air resistance acting on the body is calculated as,

$\mathrm{F=ma}$                 (3)

Inserting the values of "m" and "a" in equation (3) we get;

$\mathrm{F=1.5\times \frac{10}{3} }$

$\mathrm{F=0.5\times 10 }$

$\mathrm{F=5\ N }$

So, the air resistance acting on the body during the ascent is 5 N i.e.option(D).

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Answer 2

Concept :

This is the rate at which distance is changing or displacement is changing in a body or an object. Speed is essentially a scalar quantity, while velocity is essentially a vector quantity. It is the rate at which distance is changing or displacement is changing.

Given :

A body of mass 1.5 kg is thrown vertically upwards with an initial velocity of 40 m/s reaches its highest point after 3 s.

Find :

We have to find the air resistance acting on the body during the ascent resistance to be uniform, g = 10 m/s2.

Solution :
According to problem :

$Use kinematic equation of motion:V^2=u^2–2gh(for upward motion)0^2=(19.6)^2–2×9.8hh=19.6^2/2×9.8=19.6m.$

Hence the force exert by the air is 5N.

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