Question

Four arrows, all with the same shape and size, are shot directly upward. Ignore the effect of air resistance, but the arrows have different masses and are fired with different speeds. Rank them from highest to lowest in terms of the greatest height that they will reach. (Use only ">" or "=" symbols. Do not include any parentheses around the letters or symbols.)

A. mass = 0.0750 kg, v_initial = 21.0 m/s

B. mass = 0.125 kg, v_initial = 19.0 m/s

C. mass = 0.100 kg, v_initial = 23.0 m/s

D. mass = 0.0500 kg, v_initial = 25.0 m/s

Answer 1

Max height reached by arrows will be given by, 3rd kinematic equation:

Vf^2 = Vi^2 + 2*a*Hmax

Vf = 0 m/sec, since at max height speed of arrow will be zero

a = -g = -9.81 m/sec^2

So,

0^2 = Vi^2 - 2*g*Hmax

Hmax = Vi^2/2g

Since 'g' is constant, So max height will be directly proportional to the square of initial velocity of arrow.

from given value we can see that

V_D > V_C > V_A > V_B

Which means max height rank will be (Also see that Hmax does not depend on mass of Arrow)

Hmax_D > Hmax_C > Hmax_A > Hmax_B

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