A How Long Does It Take The Stone To Reach The Ground Vv Cos 8 15 0 M S Cos 20 0 V 14 1 M S Analyze We Have Th 1 (30.1 KiB) Viewed 27 times
A How Long Does It Take The Stone To Reach The Ground Vv Cos 8 15 0 M S Cos 20 0 V 14 1 M S Analyze We Have Th 2 (30.63 KiB) Viewed 27 times
(A) How long does it take the stone to reach the ground? VV, cos 8, (15.0 m/s) cos 20.0⁰ V = 14.1 m/s Analyze We have the information x=y= 0, y = -45.0 m, a, -g, and v, 15.0 m/s (the numerical value of y, is negative because we have chosen the top of the building as the origin). vv, sin 0,- (15.0 m/s) sin 20.0⁰ V = 5.13 m/s Find the initial x and y components of the stone's velocity: Express the vertical position of the stone from the particle under constant acceleration model: Substitute numerical values: -45.0 m = 0+ (5.13 m/s)t + (-9.80 m/s²)t² Solve the quadratic equation for t: t= X s (B) What is the speed of the stone just before it strikes the ground? VyrVy-gt Use the velocity equation in the particle under constant acceleration model to obtain the y component of the velocity of the stone just before it strikes the ground: Substitute numerical values: Vyr 5.13 m/s + (-9.80 m/s2)t m/s Use this component with the horizontal component v=V, 14.1 m/s to find the speed of the stone at t: m/s M
The following questions present a twist on the scenario above to test your understanding. Suppose another stone is thrown horizontally from the same building. If it strikes the ground 70 m away, find the following values. (a) time of flight S (b) initial speed m/s (c) speed and angle with respect to the horizontal of the velocity vector at impact m/s 0 If the stone were thrown harder, and left with 1.5 times the initial speed, you might expect it to go farther, but how exactly does that happen? (d) Throwing the stone horizontally at 1.5 times the previous speed multiplies the time to reach the ground by what factor? (e) The horizontal component of the velocity is multiplied by what factor? (f) How many times farther does the stone land from the building?
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