Question

Two stones are projected with the same speed but making different angles with the horizontal. Their ranges are equal. If the angle of projection of one is $\frac{\pi }{3}$ and its maximum height is $y_1$, then the maximum height of the other will be.

• A. $3y_1$
• B. $2y_1$
• C. $\frac{y_1}{2}$
• D. $\frac{y_1}{3}$

Answer 1

The correct option is D $\frac{y_1}{3}$

Range is the same for all complementary angles because range= u²sin2ø/g,

sin2(90-ø) = sin(180-2ø) = sin2ø.

So, the angle for the second stone will be 30°

$y_1$ = u²sin²(60°)/2g and

$y_2$ = u² sin²(30°)/2g

$y_1$/$y_2$ = (u²sin²(60°)/2g)/(u² sin²(30°)/2g)

$y_1$/$y_2$ = (3/4)/(1/4)

$y_1$/$y_2$ = 3

So, $y_2$ = $y_1$/3.