Four bodies are projected with the same velocity

Asked by admin @ 29/08/2021 in Physics viewed by 285 People

Four bodies are projected with

the same velocities at angles
30°, 40°, 55 and 65° with the
horizontal. The horizontal
range will be largest for
the
one projected at an angle
A
30
B
40
C
55°
D 65°

Answered by admin @ 29/08/2021

Answer

Formula

Range of a projectile motion is given by:

R = $U^2$ sin(2θ) / g

R is the range of projectile
θ is the angle at which it is projected
U is initial velocity
g is gravitational acceleration

So, we can say the range is directly proportional to sin(2θ)

R ∝ sin(2θ)

Method-1

Using direct values of sin(2 x 30) , sin(2 x 40), sin(2 x 55) and sin(2 x 65)

sin (60) = 0.866

sin (80) = 0.98

sin (110) = 0.93

sin (130) = 0.76

So, The horizontal range will be largest for the one projected at an angle 40°

Method-2

Without using direct values

Concept to be used-

Range projected at angle θ and at angle 90-θ will be same.

So, we can say that range of the body projected at 55° will be equal to (90-55)° = 35°

Range of the body projected at 65° will be equal to (90-65)° = 25°

Since the range is directly proportional to twice of θ,

2 x 30° = 60°

2 x 40° = 80°

2 x 35° = 70°

2 x 25° = 50°

Value of sin x always increases from 0 to 90°

Maximum value of 2θ is 80°.

So, The horizontal range will be largest for the one projected at an angle 40°

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