Question

Two balls are projected making angles of 30° and
45° respectively with horizontal. If both have same
velocity at the highest point of their path, then the
ratio of their horizontal range is...sahi answer dena koi faltu ki apni maa na chdaye thx

Answer 1

Answer:

R1/R2 = 1/√3

Explanation:

Given,

• Two balls are projected making angles of 30° and 45° respectively with horizontal.
• Both have same velocity at the highest point of their path.

At the highest point, the vertical component of velocity will be zero. Hence the horizontal velocity of two balls will be same.

u1cosø1 = u2cosø2

u1cos30 = u2cos45

u1√3/2 = u2/√2

u1/u2 = √2/√3 --------(1)

The ratio of their horizontal range will be.

R1/R2 = (u1²sin2ø1/g)/(u2²sin2ø2/g)

R1/R2 = (u1/u2)²(sin60/sin90)

R1/R2 = (2/3)(√3/2)

R1/R2 = 1/√3

R1:R2 = 1:√3

Answer 2

Answer :

• Ratio is √(3)/2 : 1

Explanation :

• Let their velocities be u
• And for First ball angle (θ1) = 30°
• For second Ball angle (θ2) = 45°

Now, for First Ball

$\longrightarrow \sf{R_1 \: = \: \dfrac{u^2 \sin 2 \theta_1}{g}} \\ \\ \longrightarrow \sf{R_1 \: = \: \dfrac{u^2 \sin 2(30^{\circ})}{g}} \\ \\ \longrightarrow \sf{R_1 \: = \: \dfrac{u^2 \sin 60^{\circ}}{g} \: \: \: \: \: \: \: ...(1)}$

______________________________

For, Second Ball

$\longrightarrow \sf{R_2 \: = \: \dfrac{u^2 \sin 2 \theta _2}{g}} \\ \\ \longrightarrow \sf{R_2 \: = \: \dfrac{u^2 \sin 2(45^{\circ})}{g}} \\ \\ \longrightarrow \sf{R_2 \: = \: \dfrac{u^2 \sin 90^{\circ}}{g} \: \: \: \: \: \: ...(2)}$

$\rule{150}{0.5}$

Divide (1) by (2)

$\longrightarrow \sf{\dfrac{R_1}{R_2} \: = \: \dfrac{\dfrac{u^2 \sin 60^{\circ}}{g}}{\dfrac{u^2 \sin 90^{\circ}}{g}}} \\ \\ \longrightarrow \sf{\dfrac{R_1}{R_2} \: = \: \dfrac{\sin 60^{\circ}}{\sin 90^{\circ}}} \\ \\ \longrightarrow \sf{\dfrac{R_1}{R_2} \: = \: \dfrac{\dfrac{\sqrt{3}}{2}}{1}} \\ \\ \underline{\underline{\sf{Ratio \: is \: \dfrac{\sqrt{3}}{2} : 1}}}$