Weight: w = mg: Acceleration of gravity: g = 9.80 m/s^2.. Two-dimensional projec

Question

Weight: w = mg: Acceleration of gravity: g = 9.80 m/s^2.. Two-dimensional projectile motion: X = X_0 + V_0x t. y = y_0 + v_0y t - 1/2gt^2. V_x = V+0x. V_y = V_oy -gt. Components of velocity: V_x = V cos. V_y = V sin. Newton's second law: F = ma. Newton's law of universal gravitation: F = G m_1 m_2/r^2. where G = 6.67 times 10^-11 Nm^2/kg^2. Maximum static friction force: f_s,max = sF_N: Kinetic friction force: f_k = kF_N. Centripetal acceleration: a_C = V^2/r. Mass of the Earth: 5.98 times 10^24 kg. Radius of the Earth: 6.38 times 10^6 m. A person throws two identical stones from the top of a cliff overlooking a lake. Stone 1 is thrown with an initial horizontal speed of 20 m/s while stone 2 is thrown with an initial horizontal speed of 40 m/s. Neglect air resistance. Stone 1 is observed to strike the surface of the lake with a vertical velocity of 30 m/s. Questions 1-6 refer to this situation. 1. Which stone hits the water first? a Stone 1; b. Stone 2; c. They hit at the same time 2. Which stone strikes the water with a greater speed? a.Stone 1; b.Stone 2; c. They strike with the same speed. 3. Immediately before they strike the water, which stone has the greater acceleration? a.Stone 1; b.Stone 2; c. They have the same acceleration.

Explanation / Answer

Here

1) as the height of the cliff is same for both the stones ,

there is no initial vertical velocity

Using second equation of motion,

y = y0 + voy * t - 0.5 * g * t^2

time taken to reach in the lake = sqrt(2 * h/g)

the time will be same for both stones

hence , the correct option is c) they hit at the same time

2) as the initial potential energy is same for both while initial kinetic energy is greater for stone 2

or using third equation of motion

v^2 - voy^2 = 2 * a * h

v^2 = voy^2 + 2 * g * h

as voy is greater for stone 2

the final energy will be greater for stone 2

hence , the stone 2 will strike the water with greater speed.

b. stone 2

3)

as the acceleration of both stones is same

acceleratio = acceleration due to gravity = 9.8 m/s^2

the correct option is c) the acceleartion will be same for both

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