At a certain moment, the angle between the velocity vector and the acceleration of a particle is greater than 90°. What can be inferred about its motion at that moment?
(1) It moves along a curve and its speed is decreasing.
(2) It moves along a straight line and accelerated.
(3) It moves along a curve and its speed is increasing.
(4) It moves along a straight line and it is decelerated.
To a stationary man, the rain is falling on his back with a velocity v at an angle with vertical. To make the rain-velocity perpendicular to the man, he:
(1) must move forward with a velocity vsin.
(2) must move forward with a velocity vtan.
(3) must move forward with a velocity vcos.
(4) should move in the backward direction.
A particle is thrown from the ground with a speed of 20 m/s at an angle 60° above the horizontal. Average velocity over its entire journey just before hitting the ground is:
(1) 10 m/s
(2) 20 m/s
(3) Zero
(4) 15 m/s
A person can throw a ball up to a maximum horizontal range of \(400~\text{m}\). The maximum height to which he can throw the ball is:
1. \(200~\text{m}\)
2. \(100~\text{m}\)
3. \(150~\text{m}\)
4. \(250~\text{m}\)
A particle is moving on a circular path of radius 1 m with a speed of 10 m/s. The magnitude of change in its velocity in the interval it subtends an angle 60° at the center is:
1. 10 m/s
2. 20 m/s
3. m/s
4. Zero
A car is moving along east at \(10\) m/s and a bus is moving along north at \(10\) m/s. The velocity of the car with respect to the bus is along:
1. | North-East | 2. | South-East |
3. | North-West | 4. | South-West |
A particle starts moving from the origin in the XY plane and its velocity after time \(t\) is given by \(\overrightarrow{{v}}=4 \hat{{i}}+2 {t} \hat{{j}}\). The trajectory of the particle is correctly shown in the figure:
1. | 2. | ||
3. | 4. |
A body A is projected vertically upwards. Another body B of the same mass is projected at an angle of 60° with the horizontal. If both the bodies attain the same maximum height, the ratio of the initial kinetic energy of body A to that of body B is:
1.
2.
3.
4.
Particles P and Q are at and . Their velocities at these positions are and respectively. If they collide after one second, then the value of c is
(1) 1
(2) 2
(3) 3
(4) 4
Two projectiles are thrown at different angles but their ranges R are the same. If their times of flight are , then the product of their times of flight is proportional to
1.
2.
3.
4. R