A boat can move with a maximum speed of 10 m/s in still water. If the speed of river water is 5 m/s, then in how much minimum time the boat can cross the river of width 500 m?
(1) s
(2) 50 s
(3) 100 s
(4) 150 s
A particle is thrown at an angle of projection = 45° with speed u. The average velocity of the particle during its ground to ground flight is
1.
2.
3.
4. 0
The raindrops are falling with speed \(v\) vertically downwards and a man is running on a horizontal road with speed \(u.\) The magnitude of the velocity of the raindrops with respect to the man is:
1. \(v-u\)
2. \(v+u\)
3. \(\sqrt{{v}^2 + {u}^2 \over 2}\)
4. \(\sqrt{{v}^2 + {u}^2}\)
A bomb is dropped from an aeroplane flying horizontally. The path of the bomb as seen by the pilot will be (neglect air friction)
(1) A straight line
(2) A parabola
(3) An ellipse
(4) A hyperbola
The range of a bullet fired from a gun at an angle with the horizontal is the same as the range of another bullet fired from that gun at an angle with the horizontal. Then,
1.
2.
3.
4.
A boy runs on a circular track of radius \(R\) (in km) with a speed of \(\dfrac{πR}{2}\) km/h in the clockwise direction for \(3\) h and then with \(πR\) km/h in the anticlockwise direction for \(1\) h. The magnitude of his displacement will be:
1. \(\dfrac{πR}{2}\)
2. \(\dfrac{R}{\sqrt{2}}\)
3. \(\dfrac{3πR}{2}\)
4. \(\sqrt{2}R\)
Two projectiles P and Q are projected with the same speed at angles 60° and 30° with horizontal on level ground, then: [R = Range, T = Time of flight, H = Maximum height]
(1)
(2)
(3)
(4) All of these
A body is projected with the same speed at two different angles covers the same horizontal distance R. If are two times of flights, then R is equal to :
1.
2.
3.
4.
A body starts moving from rest on a horizontal ground such that the position vector of the body with respect to its starting point is given by \(r= 2 t\hat{i}+3t^2\hat j\). The equation of the trajectory of the body is:
1. \(y =1.5x\)
2. \(y =0.75x^2\)
3. \(y =1.5x^2\)
4. \(y =0.45x^2\)
A particle starts moving with constant acceleration with initial velocity (\(\hat{\mathrm{i}}+5\hat{\mathrm{j}}\)) m/s. After \(4\) seconds, its velocity becomes (\(3\hat{\mathrm{i}}-2\hat{\mathrm{j}}\)) m/s. The magnitude of its displacement in 4 seconds is:
1. \(5\) m
2. \(10\) m
3. \(15\) m
4. \(20\) m