Problem 3 A ball is thrown from a position 5 ft. above ground level to the roof

Question

Problem 3 A ball is thrown from a position 5 ft. above ground level to the roof of a 100 ft. building. If the initial velocity is 110 ft/sec inclined at an angle of 60 degrees from horizontal, determine a) the maximum height h attained by the ball, and b) the horizontal distance d traveled by the ball. Ans. a) h = 146 ft b) d = 255 ft. Problem 4 The Scotch Yoke is a mechanism that transforms circular motion of a crank (2) into reciprocating motion of a slider (shaft 4). The motion is considered to be harmonic, as it is repetitive. The acceleration of point A is defined by a=-1.8 sin kt, where a is m/s'and t is sec. Also, k-3 rad/sec. If the initial conditions are x-0 at time t-0, and v-0.6 m/s at t-0, find the velocity and displacement of point A when t-0.5 sec. Let the origin be at 0 NOTE: all points on slider 4 have same velocity and acceleration, since it is rectilinear motion)

Explanation / Answer

(a)

Iniial vertical velocity, v0y = 110 sin60 = 95.26 ft/s

ay = - 32.17 ft/s^2

at maximum height vy = 0

Therefore, Applying vf^2 - vi^2 = 2 a d

0^2 - 95.26^2 = 2(-32.174) ( h)

we get, h = 141 ft

Height from Ground, H = 5+ h = 146 ft

(B)

time to travel 100 ft in vertical,

d = v0 t + a t^2 /2

100 - 5 = 95.26 t - (32.17) t^2 /2

16.09 t^2 - 95.26t + 95 = 0 ]

t = 1.2sec and 4.65 sec

it will land for the latter time.

d = v0x t = (110 cos60) (4.65) = 255.75 ft

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