Show that the maximum height and range of a projectile are U 2 sin 2 θ 2 g a n d U 2 sin 2 θ g respectively where the terms have their regular meanings.

Let a body is projected with an initial velocity ' u ' and with an angle θ to the horizontal. Initial velocity along x - d i r e c t i o n , u x = u cos θ Initial velocity along y - d i r e c t i o n , u y = u sin θ Horizontal Range: It is the distance covered by projectile along the horizontal between the point for projection to the point on ground, where the projectile returns again. It is denoted by R . The horizontal distance covered by the projectile in the to time of flight is called horizontal range. Therefore, R = u cos θ × t . R = u cos θ × 2 u sin θ g = u 2 2 sin θ cos θ g R = u 2 sin 2 θ g . . . . . ∵ 2 sin θ cos θ = sin 2 θ Angle of projection for maximum range: For a given velocity of projection, the horizontal range will be maximum, when sin 2 θ = 1 . ∴ A n g l e o f p r o j e c t i o n f o r m a x i m u m r a n g e i s 2 θ = 90 ° o r θ = 45 ° ∴ R m a x = u 2 g . Maximum height: The vertical distance covered by the projectile until its vertical component becomes zero. Applying; v 2 - u 2 = 2 a s We have, 0 - u 2 sin 2 θ = 2 - g H Maximum height reached, H = u 2 sin 2 θ 2 g

EASY

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IMPORTANT

Earn 100

Explain the terms the average velocity and instantaneous velocity. When are they equal?

Important Questions on Motion in a Plane

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 8

Show that the maximum height and range of a projectile are

\frac{U^{2} \sin^{2} θ}{2 g} a n d \frac{U^{2} \sin 2 θ}{g}

respectively where the terms have their regular meanings.

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 9

If the trajectory of a body is parabolic in one reference frame, can it be parabolic in another reference frame that moves at constant velocity with respect to the first reference frame? If the trajectory can be other than parabolic, what else can it be?

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 10

A force

2 \overset{\land}{i} + \overset{\land}{j} - \overset{\land}{k} N

acts on a body which is initially at rest. At the end of

20 seconds

the velocity of the body is

4 \overset{\land}{i} + 2 \overset{\land}{j} - 2 \overset{\land}{k} m / s .

What is the mass of the body?

MEDIUM

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 1

Ship

A i s 10 km

due west of ship

B .

Ship

A

is heading directly

n o r t h a t a s p e e d o f 30 k m / h,

while ship

B

is heading in a direction

60 ° w e s t o f n o r t h a t a s p e e d o f 20 k m / h .

Determine the magnitude of the velocity of ship

B

relative to ship

A .

MEDIUM

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 1

Ship

A

10 km

due west of ship

B .

Ship

A

is heading directly north at a speed of

30 km / h

, while ship

B

is heading in a direction

60 °

west of north at a speed of

20 km / h .

What will be their distance of closest approach?

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 2

θ

is the angle of projection,

R

the range,

h

the maximum height,

T

the time of flight then show that:
(a)

\tan θ = \frac{4 h}{R} a n d

(b)

h = \frac{g T^{2}}{8} .

EASY

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IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 3

A projectile is fired at an angle of

60 °

to the horizontal with an initial velocity of

800 m / s,

find the time of flight of the projectile before it hits the ground.

EASY

11th Telangana Board

IMPORTANT

Intermediate First Year Physics>Chapter 4 - Motion in a Plane>EXERCISES>Q 3

A projectile is fired at an angle of

60 °

to the horizontal with an initial velocity of

800 m / s,

find the distance it travels before it hits the ground.

Explain the terms the average velocity and instantaneous velocity. When are they equal?

Important Questions on Motion in a Plane

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