A projectile can have the same range R for two angles of projections at a given speed. If T 1 and T 2 be the times of flight in two cases, then find out the relation between T 1 , T 2 and R ?

Let two projectile are projected at an angle θ and α with same initial speed u under acceleration due to gravity g . For angle of projection θ , range of projectile will be given by R 1 = u 2 sin 2 θ g For angle of projection α , range of projectile will be given by, R 2 = u 2 sin 2 α g Now according to question, the range of both projectile is same, i.e., R 1 = R 2 = R ⇒ u 2 sin 2 θ g = u 2 sin 2 α g ⇒ sin 2 θ = sin 2 α But α ≠ θ , because the angle of projection of both projectile is different. ⇒ α = 90 ° - θ (complementary angles) Therefore, product of time of flights of both projectile will be given by, T 1 × T 2 = 2 u sin θ g × 2 u sin α g T 1 T 2 = 4 u 2 sin θ sin ( 90 ° - θ ) g 2 T 1 T 2 = 2 g 2 u 2 sin θ cos θ g T 1 T 2 = 2 g u 2 sin 2 θ g T 1 T 2 = 2 R g .

MEDIUM

JEE Main/Advance

IMPORTANT

Earn 100

An insect moves in a circular path of radius $R$ . If it rotates through an angle $θ$ , find its displacement, $\vec{s} = Δ \vec{r}$ , where, $Δ \vec{r}$ is the change in position vector.

Important Questions on Kinematics

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 1

Two bodies are projected at angles

A

and

(90 ° - θ)

to the horizontal with the same speed. Find the ratio of their times of flight?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 2

Two bodies are projected at angles

θ

and

(90 - θ)

to the horizontal with the same speed. Find the ratio of the maximum vertical heights?

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 3

A body is so projected in the air that the horizontal range covered by the body is equal to the maximum vertical height attained by the body during the motion. Find the angle of projection?

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 4

A projectile can have the same range

R

for two angles of projections at a given speed. If

T_{1}

and

x -

be the times of flight in two cases, then find out the relation between

T_{1}, T_{2}

and

R

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 5

A cricketer can throw a ball to a maximum horizontal distance of

100 m

. To what height above the ground can the cricketer throw the same ball with the same speed.

HARD

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 6

A player kicks a football at an angle of

45 °

with an initial speed of

20 m s^{- 1}

. A second player on the goal line

60 m

away in the direction of kick-starts running to receive the ball at that instant. Find the constant speed of the second player with which he should run to catch the ball before it hits the ground.

(g = 10 m s^{- 2})

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 7

A projectile is fired horizontally with a velocity of $98 m s^{- 1}$ from the top of a hill $490 m$ high.

$(1)$ Find the time is taken to reach the ground.

$(2)$ The distance of the target from the foot of the hill.

$(3)$ The velocity with which the particle hits the ground.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 4 - Kinematics>Exercise - 1>Q 8

From the top of a tower of height

50 m

a ball is projected upwards with a speed of

30 m s^{- 1}

at an angle of

30 °

to the horizontal. Then calculate -
(i) Maximum height from the ground.
(ii) At what distance from the foot of the tower does the projectile hit the ground.
(iii) Time of flight.

An insect moves in a circular path of radius R. If it rotates through an angle θ, find its displacement, s→=Δr→, where, Δr→ is the change in position vector.

Important Questions on Kinematics

Learn and Prepare for any exam you want !

An insect moves in a circular path of radius $R$ . If it rotates through an angle $θ$ , find its displacement, $\vec{s} = Δ \vec{r}$ , where, $Δ \vec{r}$ is the change in position vector.