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2D Kinematics

Position-time graph

         

A \( 300 \text{ g} \) football is kicked in a direction that makes a \( 30^\circ \) angle with the horizon. The above graph depicts the vertical position (in meters) of the football. If \( h_0 =80, \) how long (in seconds) does the football fly before falling back to the ground?

The air resistance is negligible and the gravitational acceleration is \( g = 10 \text{ m/s}^2.\)

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The above graph depicts the horizontal position of a ball that is thrown horizontally at \( 23 \text{ m/s} .\) If \( x_0=69 \text{ m}, \) from what height was the ball thrown?

The gravitational acceleration is \( g= 10 \text{ m/s}^2. \)

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A body of mass \( m = 3 \text{ kg} \) is projected in a direction that makes a \( \theta = 30^\circ \) angle with the horizon. The above graph shows the vertical position of the body with respect to time \(t\) (in seconds). If \(t_0= 8 \text{ s} \) and \( h_0=160 \text{ m}, \) how far does the body fly horizontally?

The air resistance is negligible and the gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

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A body of mass \( m = 1 \text{ kg} \) is projected horizontally with a velocity of \( v= 6 \text{ m/s}. \) The above graph shows the vertical position of the body with respect to time \(t\) (in seconds). If \(t_0= 8 \text{ s} ,\) from what height was the body projected?

The air resistance is negligible and the gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

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A \(9\text{ kg}\) ball is projected from the ground in a direction that makes a \( 30 ^\circ \) angle with the horizon. The above graph depicts the vertical position of the ball during its flight. If \( t_0=8\text{ s} \) and \( h_0 =80\text{ m},\) how far does the ball fly horizontally?

The air resistance is negligible and the gravitational acceleration is \( g = 10 \text{ m/s}^2. \)

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