Physic Labs

Problem 1

A small ball is launched from the edge of a cliff of height h=20h=20 m with initial speed v0=20v_0=20 m/s at 30∘30^\circ above the horizontal. Neglect air resistance and take g=10g=10 m/s2^2. Set the origin at the foot of the cliff, with xx horizontal in the launch direction and yy upward; the ground is y=0y=0. (a) Find the time from launch until impact. (b) Find the horizontal coordinate and both velocity components at impact. (c) Determine the maximum height above the ground and when it is reached.
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vy(tf)=10−10tf=−105≃−22.4 m/sv_y(t_f)=10-10t_f=-10\sqrt5\simeq-22.4\ \mathrm{m/s}
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The vertical velocity follows vy=v0y−gtv_y=v_{0y}-gt. Its negative sign confirms the ball is descending and does not alter the horizontal coordinate already found.