Answer :
Final answer:
To calculate the total travel time of the solid ball released from rest at the top of a ramp, we need to consider the motion along the ramp and the motion on the horizontal floor. The motion along the ramp can be determined using the equation for acceleration due to gravity, and the motion on the horizontal floor can be determined using the equation for distance. By adding these times together, we can calculate the total travel time.
Explanation:
To calculate the total travel time of the solid ball, we need to consider two parts of its motion: the motion along the ramp and the motion on the horizontal floor.
Motion along the ramp:
Since the ball is released from rest, we can use the equation for acceleration due to gravity to determine its speed when reaching the bottom of the ramp. The equation is given by:
v = √(2 * g * h)
Where v is the speed, g is the acceleration due to gravity (9.8 m/s^2), and h is the vertical height of the ramp.
Using the given angle of the ramp, we can calculate the vertical height:
h = length of the ramp * sin(angle)
Motion on the horizontal floor:
Once the ball reaches the bottom of the ramp, it continues rolling along the horizontal floor. The speed remains constant since no external forces act on it. We can use the equation:
distance = speed * time
to find the time taken to travel along the horizontal floor.
By adding the time for the motion along the ramp and the time for the motion on the horizontal floor, we can calculate the total travel time of the solid ball.
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