Question

A projectile is to be launched at an angle of 30° so that it falls beyond the pond of length 20 meters as shown in the figure.
a) What is the range of values of the initial velocity so that the projectile falls between points M and N?

Answer 1

Answer:

The x and y components of the displacement are given by 

x = V0 cos(θ) t       y = V0 sin(θ) t - (1/2) g t2

with θ = 22 + 10 = 32° and V0 = 15 m/s 

The relationship between the coordinate x and y on the incline is given by 

tan(10°) = y / x 

Substitute x and y by their expressions above to obtain 

tan(10°) = ( V0 sin(θ) t - (1/2) g t2) / V0 cos(θ) t 

Simplify to obtain the equation in t 

(1/2) g t + V0 cos(θ) tan(10°) - V0 sin(θ) = 0 

Solve for t

t =

 

V0 sin(θ) - V0 cos(θ) tan(10°)

0.5 g

=

 

15 sin(32°) - 15 cos(32°) tan(10°)

0.5 (9.8)

= 1.16 s

b)

OM = √[ (V0 cos(θ) t)2 + ( V0 sin(θ) t - (1/2) g t2)2 ] 

OM (t=1.16)= √[ (15 cos(32) 1.16)2 + ( 15 sin(32) 1.16 - (1/2) 9.8 (1.16)2)2 ] = 15 meters

thnq❤

Answer 2

Hope it helps and solves your problem