Question Details Suppose the stone is thrown at an angle of 31.0° below the hori

Question

Question Details
Suppose the stone is thrown at an angle of 31.0° below the horizontal from the same building (h = 46.0m) as in the example above. If it strikes the ground 51.3 m away, find the following.(Hint: For part(a), use the equation for the x-displacement to eliminate v0t from the equation for the y-displacement.
What is the:
(a) the time of flight
(b) the initial speed 6Your answer is incorrect.
(c) the speed and angle of the velocity vector with respect to the horizontal at impact
         1)  speed (m/s) is? __________________

         2)The angle is ___________ degrees below the horizontal

Explanation / Answer

Let initial speed be U m/s and time of flight be T seconds.

Horizontal component velocity = Ucos = Ucos31
Initial Vertical component velcoity = Usin = Usin31

Height = 46 m and Range = 51.3m .

X = Ucos31 x T
51.3 = Ucos31 x T

46 = ½(9.8)(T)² + Usin31xT

T = 51.3/Ucos31

46 = ½(9.8)(51.3/Ucos31)² + Usin31/(51.3/Ucos31)
46 = ½(9.8)(51.3/Ucos31)² + 51.3Tan31 '
U = 34.00 m/s
T = 1.76s

Vertical componenet at impact = 34sin31 + (1.76)(9.8) = 34.75 m/s

Speed at impact = (34cos31)² + (34.75)² =45.35 m/s
Angle =Arctan 34.75/34cos31 = 50.01 degree

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