Answer:
The magnitude of displacement is 0.082m
Explanation:
While the ball is in motion,we have MV + mv= 0 ...eq1
Where M = combined mass of the platform and the two people.
V = velocity of the platform
m = mass of the ball
v = velocity of the ball
The distance that the platform moves is given by:
X = Vt ...eq2
Where t is the time that the ball is in the air.
The time the ball is in the air is given by:
L/(v-V) ...eq3
Where L is the length of the platform
The quantity(v-V) = velocity of the ball relative to the platform.
Combining eq2 and eq3
X = (V/(v - V))L
From eq1 , the ratios of the velocities is V/v = -m/M
X = (V/v)L / (1 - (V/v) = (-m/M) L /(1+ (m/M))
X = -mL/(M + m)
X = - (3.36kg × 3.12m) /( 119kg + 3.36kg)
X = - 10.48/ 122.36
X = -0.082m
The minus sign implies that the displacement of the platform is in the opposite direction to the displacement of the ball.
Therefore, the distance moved by the platform is the magnitude of this displacement 0.082m.
Answer:
t=2s
Explanation:
The definition of power is:
And the work-energy theorem states that:
Since the movement starts from rest, we have that:
And putting all together:
Since we want the time taken:
Which for our values is:
Answer:
58,800 Joules
Explanation:
I used the formula for Potential energy which is PE = mgh
200 kg x 9.8 m/s^2 x 30 m = 58,800 J
At the very tops of the rollercoaster is maximum PE which is 58,800 J and 0 J of KE, but at the very bottom is maximum KE (kinetic energy) which is 58,800 Joules but 0 J of PE. This is because energy can not be destroyed ONLY converted
Answer:
72.53 mi/hr
Explanation:
From the question given above, the following data were obtained:
Vertical distance i.e Height (h) = 8.26 m
Horizontal distance (s) = 42.1 m
Horizontal velocity (u) =?
Next, we shall determine the time taken for the car to get to the ground.
This can be obtained as follow:
Height (h) = 8.26 m
Acceleration due to gravity (g) = 9.8 m/s²
Time (t) =?
h = ½gt²
8.26 = ½ × 9.8 × t²
8.26 = 4.9 × t²
Divide both side by 4.9
t² = 8.26 / 4.9
Take the square root of both side by
t = √(8.26 / 4.9)
t = 1.3 s
Next, we shall determine the horizontal velocity of the car. This can be obtained as follow:
Horizontal distance (s) = 42.1 m
Time (t) = 1.3 s
Horizontal velocity (u) =?
s = ut
42.1 = u × 1.3
Divide both side by 1.3
u = 42.1 / 1.3
u = 32.38 m/s
Finally, we shall convert 32.38 m/s to miles per hour (mi/hr). This can be obtained as follow:
1 m/s = 2.24 mi/hr
Therefore,
32.38 m/s = 32.38 m/s × 2.24 mi/hr / 1 m/s
32.38 m/s = 72.53 mi/hr
Thus, the car was moving at a speed of
72.53 mi/hr.