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# 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 $$g = 10 \text{ m/s}^2.$$

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 $$g= 10 \text{ m/s}^2.$$

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 $$g = 10 \text{ m/s}^2.$$

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 $$g = 10 \text{ m/s}^2.$$

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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