need help on both 7 and 8. thank you! triend\'s Frisbee has become stuck in a tr

Question

need help on both 7 and 8. thank you!

triend's Frisbee has become stuck in a tree 12 m above your throwing arm. You want to dislodge it by throwing a rock at it. You fig What speed do you have to throw the rock to bring it down? Ans: 16.13 m/s ure you need to hit it at about 5.0 m/s to dislodge it. 8. A ball (14 kg) is pitched at 90 mph. a) How much is this in m/s? b) If the bat connects with the ball and sends it into center field at 110 mph (change this to m/s). how much energy (in joules) did the bat give the ball? c) How many calories (kCals) did the batter have to eat to impart that energy? (Conversion problem) d) A fan in the stands catches it at 3 meters high from the tip of the bat. Neglecting air resistance, how fast should it be traveling?

Explanation / Answer

(7)

Given that,

h = 12 m

v = 5 m/s

From third kinematic equation,

v^2 = u^2 + 2gh

5^2 = u^2 + 2*(-9.8)*12

lnitial speed, u = 16.13 m/s

8.(a)

Given that,

m = 14 kg

vi = 90 mph

speed in m/s,

vi = 90 * 0.44704

vi = 40.23 m/s

(b)

vf = 110 mph = 49.17 m/s

Change in Kinetic energy, E = (1/2)m*(vf^2 - vi^2)

E = (1/2)*14*[(49.17)^2 - (40.23)^2]

E = 5595.9 J

(c)

E = 5595.9 * 0.000239 kCal

E = 1.33 kCal

(d)

From conservation of energy,

(1/2)m(vf^2 - vi^2) = mgh

(1/2)*(vf^2 - (40.23)^2) = 9.8*3

vf = 40.9 m/s = 91.6 mph

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