Two persons start moving along two crossroads with the same speed 5 m/s. One in the direction of north and other is in the direction of the east as shown in the figure. Angular velocity of A with respect to B is :
(1) 0.5 m/s
(2) Zero
(3) 1.0 m/s
(4) 2 m/s
In projectile motion, accelerations of the projectile when it is gaining height and losing height respectively are
(1) g upward, g upward
(2) g upward, g downward
(3) g downward, g downward
(4) g downward, g upward
A person, who can swim with speed \(u\) relative to water, wants to cross a river (of width \(d\) and water is flowing with speed \(v\)). The minimum time in which the person can do so is:
1. \(\frac{d}{v}\)
2. \(\frac{d}{u}\)
3. \(\frac{d}{\sqrt{v^{2} + u^{2}}}\)
4. \(\frac{d}{\sqrt{v^{2} - u^{2}}}\)
The position vector of a particle \(\overrightarrow r\) as a function of time \(t\) (in seconds) is \(\overrightarrow r=3 t \hat{i}+2t^2\hat j~\text{m}\). The initial acceleration of the particle is:
1. \(2~\text{m/s}^2\)
2. \(3~\text{m/s}^2\)
3. \(4~\text{m/s}^2\)
4. zero
Velocity and acceleration vectors of a particle moving on a circular path are shown here. At the instant shown:
(1) The speed of the particle must be decreasing.
(2) Acceleration of particle must be increasing in magnitude.
(3) The dot product of and is positive.
(4) The magnitude of the momentum of the particle must be increasing in magnitude.
A cricketer can throw a ball to a maximum horizontal distance of 50 m. How much high above the ground can he throw the same ball?
(1) 50 m
(2) 25 m
(3) 75 m
(4) 100 m
Coordinates of a particle as a function of time \(t\) are \(x= 2t\),
\(y =4t\). It can be inferred that the path of the particle will be:
1. | Straight line
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2. | Ellipse
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3. | Parabola
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4. | Hyperbola |
When a man walks on a horizontal road with velocity \(1\) km/h, the rain appears to him coming vertically at a speed of \(2\) km/h. The actual speed of the rain with respect to ground is:
1. \(\sqrt{3}\) km/h
2. \(\sqrt{5}\) km/h
3. \(1\) km/h
4. \(3\) km/h
Path of a projectile as seen from another projectile :
(1) Straight
(2) Circular
(3) Hyperbolic
(4) Parabolic