Answer :
Based on the provided information, the ball was released at a height of 1.64 meters and reached a maximum height of 3.35 meters. The vertical displacement from the release height to the maximum height is 2.22 meters.
Based on the provided information, we can analyze the motion of the ball. The initial height of the ball can be estimated as 1.64 meters since it was released from the student's hand at that height. After 0.61 seconds, the ball reached its maximum height of 3.35 meters.
To determine additional details about the ball's motion, we can use the principles of projectile motion. When an object is thrown upwards, its motion can be divided into two components: vertical and horizontal. The vertical component is influenced by gravity, while the horizontal component remains constant.
Let's consider the vertical motion of the ball. The time taken to reach the maximum height is the same as the time taken to descend from the maximum height to the release height. Hence, the total time of flight is 0.61 seconds x 2 = 1.22 seconds.
Using the equation for vertical displacement (Δy) in projectile motion:
Δy = v₀y × t - 0.5 × g × t²
where v₀y is the initial vertical velocity and g is the acceleration due to gravity (-9.8 m/s²), we can solve for the initial vertical velocity.
At the maximum height, the vertical velocity becomes zero since the ball momentarily stops before descending. Hence, using the equation for vertical velocity (vₓ):
vₓ = v₀y - g × t
0 = v₀y - 9.8 × 0.61
v₀y = 5.978 m/s
Now, we can calculate the vertical displacement from the release height to the maximum height:
Δy = v₀y × t - 0.5 × g × t²
Δy = 5.978 × 0.61 - 0.5 × 9.8 × (0.61)²
Δy = 3.35 - 0.568 - 0.561
Δy = 2.22 meters
Therefore, the vertical displacement from the release height to the maximum height is 2.22 meters.
In conclusion, based on the provided information, the ball was released at a height of 1.64 meters and reached a maximum height of 3.35 meters. The vertical displacement from the release height to the maximum height is 2.22 meters. These calculations are based on the principles of projectile motion, considering the effects of gravity.
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