Advertisements
Advertisements
Question
A ball is projected from a point on the floor with a speed of 15 m/s at an angle of 60° with the horizontal. Will it hit a vertical wall 5 m away from the point of projection and perpendicular to the plane of projection without hitting the floor? Will the answer differ if the wall is 22 m away?
Advertisements
Solution
Given:
Initial speed of the ball, u = 15 m/s
The angle of projection with horizontal, α = 60°
Distance of the wall from the point of projection = 5 m
a = g = 9.8 m/s2 (Acceleration due to gravity)
We know that the horizontal range for a projectile is given by
\[R = \frac{u^2 \sin2\alpha}{g}\]
\[\Rightarrow R = \frac{{15}^2 \times \sin\left( 2 \times 60^\circ \right)}{9 . 8} = 19 . 88 \text{ m } \]
In the first case, the wall is 5m away from the projection point, so it is in the horizontal range of the projectile. So the ball will hit the wall. In the second case (22 m away), the wall is not within the horizontal range. So the ball would not hit the wall.
APPEARS IN
RELATED QUESTIONS
A ball is dropped from a height of 90 m on a floor. At each collision with the floor, the ball loses one tenth of its speed. Plot the speed-time graph of its motion between t = 0 to 12 s.
The velocity of a particle is towards west at an instant. Its acceleration is not towards west, not towards east, not towards north and towards south. Give an example of this type of motion .
Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Which bullet will hit he ground first?
A train starts from rest and moves with a constant acceleration of 2.0 m/s2 for half a minute. The brakes are then applied and the train comes to rest in one minute. Find the maximum speed attained by the train .
Complete the following table:
| Car Model | Driver X Reaction time 0.20 s |
Driver Y Reaction time 0.30 s |
| A (deceleration on hard braking = 6.0 m/s2) | Speed = 54 km/h Braking distance a = ............ Total stopping distance b = ............ |
Speed = 72 km/h Braking distance c = ........... Total stopping distance d = ............ |
| B (deceleration on hard braking = 7.5 m/s2) | Speed = 54 km/h Breaking distance e = ........... Total stopping distance f = ............ |
Speed 72 km/h Braking distance g = ............. Total stopping distance h = ............ |
A police jeep is chasing a culprit going on a motorbike. The motorbike crosses a turning at a speed of 72 km/h. The jeep follows it at a speed of 90 km/h, crossing the turning ten seconds later than the bike. Assuming that they travel at constant speeds, how far from the turning will the jeep catch up with the bike?
A stone is thrown vertically upward with a speed of 28 m/s. Find the maximum height reached by the stone.
An elevator is descending with uniform acceleration. To measure the acceleration, a person in the elevator drops a coin at the moment the elevator starts. The coin is 6 ft above the floor of the elevator at the time it is dropped. The person observes that the coin strikes the floor in 1 second. Calculate from these data the acceleration of the elevator.
In a soccer practice session the football is kept at the centre of the filed 40 yards from the 10 ft high goalposts. A goal is attempted by kicking the football at a speed of 64 ft/s at an angle of 45° to the horizontal. Will the ball reach the goal post?
A person standing on the top of a cliff 171 ft high has to throw a packet to his friend standing on the ground 228 ft horizontally away. If he throws the packet directly aiming at the friend with a speed of 15.0 ft/s, how short will the packet fall?
A staircase contains three steps each 10 cm high and 20 cm wide (in the following figure). What should be the minimum horizontal velocity of a ball rolling of the uppermost plane so as to hit directly the lowest plane?
A man is sitting on the shore of a river. He is in the line of 1.0 m long boat and is 5.5 m away from the centre of the boat. He wishes to throw an apple into the boat. If he can throw the apple only with a speed of 10 m/s, find the minimum and maximum angles of projection for successful shot. Assume that the point of projection and the edge of the boat are in the same horizontal level.
A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. If he heads in a direction making an angle θ with the flow, find the time he takes to cross the river.
A swimmer wishes to cross a 500 m wide river flowing at 5 km/h. His speed with respect to water is 3 km/h. Find the shortest possible time to cross the river.
An aeroplane has to go from a point A to another point B, 500 km away due 30° east of north. A wind is blowing due north at a speed of 20 m/s. The air-speed of the plane is 150 m/s. Find the direction in which the pilot should head the plane to reach the point B.
A ball is dropped from a building of height 45 m. Simultaneously another ball is thrown up with a speed 40 m/s. Calculate the relative speed of the balls as a function of time.
A man is standing on top of a building 100 m high. He throws two balls vertically, one at t = 0 and other after a time interval (less than 2 seconds). The later ball is thrown at a velocity of half the first. The vertical gap between first and second ball is +15 m at t = 2 s. The gap is found to remain constant. Calculate the velocity with which the balls were thrown and the exact time interval between their throw.
