Gravitation Worksheet-3
A. u = 19.6 m/s t = 2 s B. u = 9.8 m/s t = 2 s
C. u = 19.6 m/s t = 4 s D. u = 9.8 m/s t = 4 s
(a) Calculate the speed of the ball when it hits the ground.
(b) Calculate the time it takes to fall through this height. (g = 10 m/s^{2})
A. v = 20 m/s t = 2 s B. v = 20 m/s t = 4 s
C. v = 20 m/s t = 1 s D. v = 10 m/s t = 2 s
A. 15 m B. 10 m C. 12 m D. None of these
A. 49 N B. 49 kg C. 5 kg D. None of these
A. 6 kg B. 49 kg C. 5 N D. 5 kg
Answer Key:
Explanation: Here, the ball is moving up against the attraction of earth, so its velocity will decrease continuously or we can say that the ball is being retarded.
Thus, the acceleration in the ball is negative which means that the value of g will be used here with the negative sign.
Here, Initial velocity of ball, u = ?
Final velocity of ball, v = 0 (As it stops)
Acceleration due to gravity, g = -9.8 m/s^{2} (Ball is going up)
And, Height, h = 19.6 m
Now, putting all these values in the formula :
v^{2} = u^{2} + 2gh
We get : (0)^{2} = u^{2} + 2 × (–9.8) × 19.6
0 = u^{2} – 19.6 × 19.6
u^{2} = (19.6)^{2}
So, u = 19.6 m/s
Thus, the initial velocity of the ball is 19.6 m/s which means that the ball has been thrown upwards with a velocity of 19.6 m/s.
The time taken can be calculated by using the equation:
v = u + gt
Here, Final velocity, v = 0 (The ball stops)
Initial velocity, u = 19.6 m/s (Calculated )
Acceleration due to gravity, g = –9.8 m/s^{2} (Ball is going up)
And, Time, t = ?
So, putting these values in the above equation, we get :
0 = 19.6 + (-9.8) x t
0 = 19.6 – 9.8 t
9.8 t = 19.6
t = (19.6/9.8)
t = 2 s
hence, the ball takes 2 seconds to reach the highest point of its upward journey. The ball will take an equal time, that is, 2 seconds to fall back to the ground. In all the ball will take a total of 2 + 2 = 4 seconds to reach back to the thrower.
Explanation: (a) initial speed, u = 0
Final speed, v = ?
Acceleration due to gravity, g = 10 m/s^{2} (ball is coming down)
And, Height, h = 20 m
Now, we know that for a freely falling body :
v^{2} = u^{2} + 2gh
So, v^{2} = (0)^{2} + 2 × 10 × 20
v^{2} = 400
Or v = 20 m/s
Thus, the speed of cricket ball when it hits the ground will be 20 metres per second.
(b) Now, initial speed, u = 0
Final speed, v = 20 m/s (Calculated )
Acceleration due to gravity, g = 10 m/s^{2}
And, Time, t = ?
Putting the values in the formula :
v = u + gt
We get: 20 = 0 + 10 x t
10 t = 20
t = (20/10)
t = 2 s
thus, the ball takes 2 seconds to fall through a height of 20 metres.
Explanation: Since the ball is going up against the gravity, so the value of g will be taken as negative.
Here, initial speed of ball, u = 15 m/s
Final speed of ball, v = 0 (The ball stops)
Acceleration due to gravity, g = -9.8 m/s^{2} (Retardation)
And, Height, h = ?
Now, putting all these values in the formula,
v^{2} = u^{2} + 2gh,
(0)^{2} = (15)^{2} + 2 × (–9.8) × h
0 = 225 – 19.6 h
19.6 h = 225
Or h = (225/19.6)
h = 11.4 m
Hence the ball will go to a height of 11.4 metres before it starts falling.
Explanation: Weght, W = m × g
Here, mass of the body, m = 5 kg
And, acceleration due to gravity, g = 9.8 m/s^{2}
So, weight, W = 5 × 9.8 = 49 N
Thus, the weight of the body is 49 newtons.
Explanation: Here, weight, W = 49 N
Mass, m = ?
And, Acceleration due to gravity, g = 9.8 m/s^{2}
Now, putting these values in the formula,
W = m × g
We get : 49 = m × 9.8
m = (49/9.8)
m = 5 kg
Thus, the mass of the object is 5 kilograms.