An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio:

Question

An object is projected at an angle of 45° with the horizontal. The horizontal range and maximum height reached will be in the ratio: (A)  1:2  (B)  2:1  (C)  1:4  (D)  4:1

Tardigrade Admin · Accepted Answer

Horizontal range, R=(u2 sin 2× 45/g) =(u2/g) Maximum height, h=(u2 sin 245/2g) =(u2/4g) (R/h)=(4/1)

Q. An object is projected at an angle of $45^{\circ}$ with the horizontal. The horizontal range and maximum height reached will be in the ratio:

$1 : 2$

$2 : 1$

$1 : 4$

$4 : 1$

$4 : 2$

Horizontal range, $R = \frac{u ^{2} s i n 2 \times 45}{g}$
$= \frac{u ^{2}}{g}$
Maximum height, $h = \frac{u ^{2} s i n ^{2} 45}{2 g}$
$= \frac{u ^{2}}{4 g}$
$\frac{R}{h} = \frac{4}{1}$

Q. An object is projected at an angle of 45∘ with the horizontal. The horizontal range and maximum height reached will be in the ratio:

1:2

2:1

1:4

4:1

4:2​

Horizontal range, R=gu2sin2×45​ =gu2​ Maximum height, h=2gu2sin245​ =4gu2​ hR​=14​