High School

A student estimated, based on the video, that the ball left the hand at a height of 1.64 meters off the ground. After 0.6 seconds, the ball reached its maximum height of 3.28 meters.

Use this information to find an equation for the height \( h \) of the ball, in meters, after \( t \) seconds.

Answer :

Final answer:

The equation for the height of the ball is h = 1.64 - (9.8)(0.18) after 0.6 seconds. A negative height doesn't make physical sense in this context, suggesting there may be an error in the calculations or estimation.

Explanation:

To find an equation for the height of the ball, we need to use the kinematic equation for vertical motion. The equation is given as:

h = h0 + v0t - ½gt2

Where:

  • h is the height of the ball
  • h0 is the initial height (1.64 meters)
  • v0 is the initial vertical velocity (0 m/s)
  • t is the time in seconds (0.6 seconds)
  • g is the acceleration due to gravity (9.8 m/s2)

Plugging in the values, the equation becomes:

h = 1.64 + (0)(0.6) - ½(9.8)(0.62)

Simplifying the equation gives:

h = 1.64 - (9.8)(0.18)

Therefore, the equation for the height of the ball is h = 1.64 - 1.764 = -0.124 meters after 0.6 seconds. However, it's important to note that a negative height doesn't make physical sense in this context, so it's likely there was an error in the calculations or estimation.

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