Motion In Two Dimension Test

Result

Motion In Two Dimension Test - 4

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Weekly Quiz Competition

Question 1
4 / -1

A stone projected with a velocity u at an angle θ with the horizontal reaches maximum height H₁. When it is projected with velocity u at an angle (2/π −θ) with the horizontal, it reaches maximum height H₂. The relation between the horizontal range R of the projectile, H₁ and H₂ is

A

B
R = 4 (H₁ + H₂)

C
R = 4 (H₁ - H₂)

D

Solution
Question 2
4 / -1

A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. Find the ratio of their velocities when they reach the earth's surface.

A
1:1

B
2:1

C
3:1

D
1:2

Solution
Question 3
4 / -1

A particle is projected from point O with velocity u in a direction making an angle α with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is

A
u tan ⁡α

B
u cot⁡ α

C
u cosec⁡ α

D
u sec⁡ α

Solution

Horizontal velocity at point ′O′ = u cos ⁡α

Horizontal velocity at Point ′P′ = v sin ⁡α

In projectile motion horizontal component of velocity remains constant throughout the motion

∴ v sin ⁡α = u cos ⁡α

⇒ v = u cot ⁡α
Question 4
4 / -1

Pankaj and Sudhir are playing with two different balls of masses m and 2m, respectively. If Pankaj throws his ball vertically up and Sudhir at an angle θ with the verticle, both of them stay in our view for the same period. The height attained by the two balls are in the ratio

A
2:1

B
1:1

C
1 : cos θ

D
1 : sec θ

Solution
Question 5
4 / -1

A ship ,4 sailing due east with a velocity of 10 km/h happens to appear sailing due north with a velocity of 5 km/h , to a person, sitting in a moving ship B. Determine the velocity (absolute) of ship B.

A

B

C

D

Solution
Question 6
4 / -1

A particle is projected with certain velocity at an angle α above the horizontal from the foot of an inclied plane of inclination 30⁰ . If the particle strikes the plane normally then α is

A

B
45⁰

C
60⁰

D

Solution

If the projectile hits the incline normally, it means that component of velocity along the incline is zero.
Question 7
4 / -1

Two balls A and B are thrown with speeds u and u/2, respectively. Both the balls cover the same horizontal distance before returning to the plane of projection. If the
angle of projection of ball ,B is 15^o with the horizontal, then the angle of Projection of A is

A

B

C

D

Solution
Question 8
4 / -1

A boy projects a stone vertically perpendicular to the trolley car with a speed v. If the trolley car moves with a constant velocity u, the time of flight of the stone is:

A
u+v / g

B
2v / g

C
2u / g

D
none of these

Solution

Time of flight depends on vertical component of velocity.
Question 9
4 / -1

A bird is flying towards north with a velocity 40 kmh⁻¹ and a train is moving with velocity 40 kmh⁻¹ towards east. What is the velocity of the bird noted by a man in the train?

A
40√2 kmh^-1 N – E

B
40√2 kmh^-1 S – E

C
40√2 kmh^-1 N – W

D
40√2 kmh^-1 S – W

Solution
Question 10
4 / -1

A person walks at the rate of 3 km/hr. Rain appears to him in vertical direction at the rate of 3√3km/hr. Find the magnitude and direction of true velocity of rain.

A
6 km/hr, inclined at an angle of 45^o to the vertical towards the person's motion.

B
3 km/hr, inclined at an angle of 30o to the vertical towards the person's motion.

C
6 km/hr, inclined at an angle of 30^o to the vertical towards the person's motion.

D
6 km/hr, inclined at an angle of 60^o to the vertical towards the person's motion.

Solution