Question

1. Three masses, 25g, 50g, 75g, have cover a force table at angles 0^o, 90^o, 180^o respectively. (a) find the magnitude and the angle of the resultant force, graphically (b) Find the magnitude and the angle of the resultant force, analytically. (c) Calculate the % error between the two methods using the analytical as the theoretical value.

2. A projectile is launched at an angle of 35^o, with an intial velocity 25 m/s. It strikes the ground 20 meters lower than the initial launch position (a) how long was the projectile in flight? (b) what was the maximum height the projectile reaches.

Answer 1

2.

Given that Vi = 25 m/sec at 35 deg

Vix = Vi*cos A = 25*cos 35 deg = 20.48 m/sec

Viy = Vi*sin A = 25*sin 35 deg = 14.34 m/sec

Now using equation

h = Viy*t + 0.5*a*t^2

a = -g = -9.8 m/sec^2

h = -20 m

-20 = 14.34*t - 0.5*9.8*t^2

4.9*t^2 - 14.34*t - 20 = 0

Solving above quadratic equation

t = [14.34 +/- sqrt (14.34^2 + 4*20*2.9)]/(2*4.9) = 3.597 sec

t = 3.6 sec

Part B

Max height in projectile motion is given by:

Hmax = V0^2*(sin A)^2/(2*g) = Viy^2/2g

Hmax = 14.34^2/(2*9.8) = 10.5 m

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