a ball rolls off a desk at a speed of 3.0m/s and lands 0.40 seconds later. How far from the base of the desk does the ball lands?
since the horizontal speed does not change, the distance is
3.0 m/s * 0.40s = 1.2 m
To find the distance from the base of the desk where the ball lands, we can use the equation of motion:
d = v * t
Where:
d = distance
v = initial velocity
t = time
Given:
v = 3.0 m/s
t = 0.40 s
Substituting the given values into the equation, we get:
d = 3.0 m/s * 0.40 s
Now, we can calculate the distance:
d = 1.2 meters
Therefore, the ball lands 1.2 meters from the base of the desk.
To find the distance the ball lands from the base of the desk, we can use the formula for the vertical motion of an object:
d = v * t + (1/2) * g * t^2
Where:
d is the distance traveled
v is the initial velocity in the vertical direction
t is the time of flight
g is the acceleration due to gravity (approximately 9.8 m/s^2)
In this case, the initial velocity, v, is 3.0 m/s and the time of flight, t, is 0.40 seconds. We can now calculate the distance, d, using the formula.
d = (3.0 m/s) * (0.40 s) + (1/2) * (9.8 m/s^2) * (0.40 s)^2
d = 1.2 m + (1/2) * (9.8 m/s^2) * (0.16 s^2)
d = 1.2 m + 0.784 m
d = 1.984 m
Therefore, the ball lands approximately 1.984 meters from the base of the desk.