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A balll is projected with initial speed of 40 m/s making an angle of 30 degrees with the horizontal. Find (1) Vertical displacement (2) Horizontal displacement (3) velocity and angle it is making with horizontal at t=1 and t=3 sec.

A balll is projected with initial speed of 40 m/s making an angle of 30 degrees with the horizontal. Find
(1) Vertical displacement
(2) Horizontal displacement
(3) velocity and angle it is making with horizontal at t=1 and t=3 sec.

Grade:12th pass

1 Answers

Eshan
askIITians Faculty 2095 Points
3 years ago
Dear student,

The horizontal and vertical componetns of veloicty are

u_x=ucos30^{\circ}=\dfrac{\sqrt{3}}{2}u
andu_y=usin30^{\circ}=\dfrac{1}{2}u

Therefore vertical displacement in time 't’=u_yt-\dfrac{1}{2}gt^2
Horizontal displacement in time ‘t’=u_xt

Horizontal component of velocity after time ‘t’=v_x=u_x(since no force acts in the horizontal direction)

Vertical component of velocity=v_y=u_y-gt

Hence angle velocity forms with horizontal after time ‘t’=tan^{-1}(\dfrac{v_y}{v_x})=tan^{-1}(\dfrac{u_y-gt}{u_x})

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