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Please provide a step-wise solution.
A projectile (m=2kg) is shot from a cannon at an initial angle of θ=30° with an initial speed of vo=40m/s. Assume the ball is shot from the origin.© BrainMass Inc. brainmass.com December 16, 2022, 5:48 am ad1c9bdddf
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a) Maximum height reached by the projectile is given by: H = u^2 sin^2 θ/2g
Substituting u = 40 m/s, θ = 30^O we get: H = 40^2 sin^2 30^O /2x9.8 = 20.41 m
Maximum height reached = 20.41 m
To determine the time taken to reach the maximum height, we note that the vertical component of the initial velocity u_y = usin30^O = 40sin30^O = 20 m/s
As the projectile moves up, it is subjected to a vertical retardation of g = - 9.8 m/s^2
We now determine the time taken by the projectile to cover a distance of 20.41 m, starting with a vertical velocity of 20 m/s and decelerating at - 9.8 m/s^2. Applying the kinematic equation y = u_y t + ½ at^2 we get: 20.41 = 20t - ½ x 9.8 x t^2
4.9t^2 - 20t + 20.41 = 0
Solving for t: t = [- (- 20) + √(- 20)^2 - 4(4.9)(20.41)]/2(4.9)
t = [+ 20 + √400 - 400]/9.8 = 20/9.8 = 2.04 sec
Projectile takes 2.04 ...
This solution provides detailed explanations of how to determine a projectile's trajectory based on it's angle and initial speed. A number of other measures are determined in this tutorial.