Question

10) An object is propelled upward at an angle e, 45° << 90°, to the horizontal with an initial velocity of vo feet per second from the base of a plane that makes an angle of 45° with the horizontal. If air resistance is ignored, th distance R that it travels up the inclined plane is given by the function vo22 R(O) = [sin(20) - COS(20) - 11. 32 Show that v02/2 R(O) = [sin (cos 0 + sin o) - 1). 16

Answer 1

Solution

From the given data we have,

R(θ) =V₀²√2 [ sin(2θ)-cos(2θ)-1]/32 where R(θ) is the distance traveled up the incline,

in the above equation let,

V₀²√2 / 32 =A (for mathematical convinience while solving and representation)

thus

R(θ)= A[sin(2θ)-cos(2θ)-1]

but sin(2θ) =2sinθcosθ

cos2θ = 1-2sin²θ

substituting the above values in given equation we get,

R(θ) = A[2sinθcosθ-1+2sin²θ-1]

=>R(θ)=2A[sinθcosθ+sin²θ-1]

=>R(θ)=2A[sinθ(sinθ+cosθ)-1] , substituting the value of A we get,

R(θ) =2(V₀²√2 / 32)[sinθ(sinθ+cosθ)-1]

=>R(θ) =V₀²√2[sinθ(sinθ+cosθ)-1]/16 ;which is required to prove hence PROVED ....(answer)