Kinematics

JEE Main level, single correct, medium

200 of 308

Question 200 of 308

If xx and yy coordinates of a projectile as a function of time (t)(t) are given as 24t24t and 43.6t−4.9t243.6t-4.9t^2, respectively, then the angle (in degrees) made by the projectile with horizontal when t=2t=2 s is ______.

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Answer: (B) 4545

The velocity components of the projectile are given by the derivatives of the position coordinates with respect to time.

vx=dxdt=ddt(24t)=24v_x = \dfrac{dx}{dt} = \dfrac{d}{dt}(24t) = 24

vy=dydt=ddt(43.6t−4.9t2)=43.6−9.8tv_y = \dfrac{dy}{dt} = \dfrac{d}{dt}(43.6t - 4.9t^2) = 43.6 - 9.8t

At t=2t = 2 s, the velocity components are:

vx=24v_x = 24

vy=43.6−9.8(2)=43.6−19.6=24v_y = 43.6 - 9.8(2) = 43.6 - 19.6 = 24

The angle θ\theta made by the velocity vector with the horizontal is given by:

tan⁡θ=vyvx=2424=1\tan \theta = \dfrac{v_y}{v_x} = \dfrac{24}{24} = 1

θ=45∘\theta = 45^{\circ}

Answer: 4545

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