Physics: * A ball is projected horizontally from the top of a building 19.6m high.a, How long when the ball take to hit the ground?b, If the line joining the point of projection tothe point where it hits the ground is 45with the horizontal. What must be theinitial velocity of the ball?c,with what vertical verocity does the ball strikethe grounds? (9= 9.8 M152)

The velocity from the displacement time graph is finding the slope of the graph for the required time....

* A ball is projected horizontally from the top

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30.07.2021

Explanation:

Given

Ball is projected horizontally from a building of height $h=19.6\ m$

time taken to reach ground is given by

$\text{Cosidering vertical motion}\\\Rightarrow h=ut+0.5at^2\\\Rightarrow 19.6=0+0.5\times 9.8t^2\\\Rightarrow t^2=4\\\Rightarrow t=2\ s$

(b) Line joining the point of projection and the point where it hits the ground makes an angle of $45^{\circ}$

From the figure, it can be written

$\Rightarrow \tan 45^{\circ}=\dfrac{h}{x}\\\\\Rightarrow x=h\cdot 1\\\Rightarrow x=19.6$

Considering horizontal motion

$\Rightarrow x=u_xt\\\Rightarrow 19.6=u_x\times 4\\\Rightarrow u_x=4.9\ m/s$

$\Rightarrow v^2-u_y^2=2as\\\Rightarrow v^2-0=2\times 9.8\times 19.6\\\Rightarrow v=\sqrt{384.16}\\\Rightarrow v=19.6\ m/s$

Thus, the ball strikes with a vertical velocity of $19.6\ m/s$

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