Question

A projectile is launched ${30.0}^o$ above the horizontal from the top of a tower with an initial speed of $10.0m/s$.
After $2.00seconds$, approximately how much total displacement will the projectile have experienced?
Take air resistance to be negligible and gravity to be the only source of acceleration.

• A. $10.0m$
• B. $17.3m$
• C. $19.6m$
• D. $19.8m$
• E. $20.0m$

Answer 1

Answer: (B)

$17.3m$

Given : $\theta ={30}^o$ $u=10$ m/s

From figure, $u_x=ucos{30}^o=10\times 0.866=8.66$ m/s

Also $u_y=usins{30}^o=10\times 0.5=5$ m/s

x-direction : $a_x=0$ $m/s^2$

Thus displacement in x direction in $t=2$ s, $S_x=u_{x}t=8.66\times 2=17.3$ m

y-direction : $a_y=-g=-10$ $m/s^2$

Thus displacement in y direction in $t=2$ s, $S_y=u_{y}t+\frac{1}{2}{a}_y{t}^2$

$\therefore$ $S_y=10\times 2-\frac{1}{2}\times 10\times 2^2=0$ m

$⟹$ Total displacement $S_T=\sqrt{S_y^2+S_x^2}=\sqrt{0+(17.3{)}^2}=17.3$ m