A projectile is launched with an initial speed of at an angle of above the horizontal

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

A projectile is launched with an initial speed of

25\text{ m/s}

at an angle of

60^{\circ}

above the horizontal. Its flight is modeled (neglecting air resistance) by the parametric equations

x(t)=25\cos 60^{\circ}\,t

and

y(t)=25\sin 60^{\circ}\,t-\tfrac{1}{2}(9.8) t^{2}

, where

t

is measured in seconds. Determine the numerical value of

\dfrac{d^{2}y}{dx^{2}}

(in

\text{m}^{-1}

) at

t=2\text{ s}

. (a)

-0.784

(b)

0.063

(c)

-0.063

(d)

-4.9