(10%) Problem 7: A baseball of mass m1 = 0.46 kg is thrown at another ball hangi

Question

(10%) Problem 7: A baseball of mass m1 = 0.46 kg is thrown at another ball hanging from the ceiling by a length of string L 1.3 m. The second ball m12- 0.84 kg is initially at rest while the baseball has an initial horizontal velocity of V 2.5 m/s. After the collision the first baseball falls straight down (no horizontal velocity.) Randomized Variables m 0.46 kg m2 = 0.84 kg L=1.3m V1=2.5m/s 2Otheexpertta.com 50% Part (a) Select an expression for the magnitude of the closest distance from the ceiling the second ball will reach d Grade Summary 7721 ½ 0% 100% Submissions Attempts remaining: 3 5% per attempt) detailed view Submit I give up! Hints: 1 % deduction per hint. Hints remaining: 2 Feedback: 1% deduction per feedback. 50% Part (b) What is the angle that the string makes with the vertical at the highest point of travel in degrees?

Explanation / Answer

here,

m1 = 0.46 kg

m2 = 0.84 kg

initial speed of first ball , v1 = 2.5 m/s

let the speed of seccond ball afetr the collison be v

using conservation of momentum

m1 * v1- m2 * v = 0

v = m1 * v1 /m2

and

let the height above the initial position be h0

using conservation of energy

m2 * g * h0 = 0.5 * m2 * v^2

h0 = ( m1 * v1/m2)^2 /( 2g)

a)

the height from the ceiling, d = L - h0

d = L - ( m1 * v1)^2 /( 2g*m2^2)

b)

d = 1.3 - ( 0.46 * 2.5)^2 /( 2 * 9.81 * 0.84^2)

d = 1.2 m

theta = arccos(d/L) = 22.6 degree

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