A ball is projected horizontally from the edge of a table that is 0.465 m high, and it strikes the floor at a point 1.04 m from the base of the table.
gravity is 9.8 m/s
the initial speed of the ball is 3.376042 m/s
~How high is the ball above the floor when its
velocity vector makes a −33.3153◦
angle with the horizontal?
Answer in units of m.
To determine the height above the floor when the velocity vector of the ball makes a -33.3153° angle with the horizontal, we can use the projectile motion equations.
Step 1: Find the vertical component of velocity (Vy).
Since the angle is measured with the horizontal, we can use the sine function:
sin(-33.3153°) = Vy / initial velocity
Vy = initial velocity * sin(-33.3153°)
Step 2: Find the time of flight (t).
The time of flight can be found using the equation:
t = 2 * (vertical displacement) / gravity
Since the ball is projected horizontally, the vertical displacement is equal to the height of the table.
Step 3: Find the vertical displacement of the ball.
The vertical displacement can be found using the equation:
(vertical displacement) = (initial velocity * sin(θ)) * t - (0.5 * gravity * t^2)
Note: θ is the angle we are given, which is -33.3153°.
Now, let's calculate the values step by step.
Step 1:
Vy = 3.376042 m/s * sin(-33.3153°)
Vy ≈ -1.833789 m/s (negative sign indicates motion in the downward direction)
Step 2:
t = 2 * (0.465 m) / 9.8 m/s^2
t ≈ 0.095 sec
Step 3:
(vertical displacement) ≈ (3.376042 m/s * sin(-33.3153°)) * 0.095 sec - (0.5 * 9.8 m/s^2 * (0.095 sec)^2)
Now, let's calculate the value of (vertical displacement).
(vertical displacement) ≈ (-1.833789 m/s) * 0.095 sec - (0.5 * 9.8 m/s^2 * (0.009025 sec^2)
(vertical displacement) ≈ -0.174 m
Therefore, the height of the ball above the floor when its velocity vector makes a -33.3153° angle with the horizontal is approximately 0.174 meters.