1. A rocket is launched vertically at time t = 0. The elevation of the rocket is given by y = -0.13t* + 4.1t³ + 0.12t² m where t is in seconds. Determine the maximum velocity V of the rocket in m/s and the elevation E at which it occurs in m.

v(3) A crate of mass m = 10 kg is "lifted" from rest by a rope with a force given by F = 75√t N. Find the speed of the box at t = 3 s and at t = 6 s. How much higher is the box, measured from its starting position, at t = 6 s? Use impulse and momentum, I guess = v(6) = y(6) m S m 8 m m F CC UBC Engineering

A helicopter with a mass of 10,000 kg takes off straight up at t=0. The thrust of the engine is defined given as a function of time: FT= 95 0.18t- (kN). Where t is in units of seconds. How fast is it rising and what is its elevation at t=4s?

Gas guns are used to investigate the properties of materi- als subjected to high-velocity impacts. A projectile is accelerated through the barrel of the gun by gas at high pressure. Assume that the acceleration of the projectile in m/s² is given by a = c/s, where s is the position of the projectile in the barrel in meters and c is a constant that depends on the initial gas pressure behind the projectile. The projectile starts from rest at s = 1.5 m and acceler- ates until it reaches the end of the barrel at s = 3 m. Determine the value of the constant c necessary for the projectile to leave the barrel with a velocity of 200 m/s.

Q5

At the instant of vertical launch, the rocket expels exhaust at the rate of 250 kg/s with an exhaust velocity of 855 m/s. If the initial vertical acceleration is 4.3 m/s. Calculate the total mass of the rocket and fuel in kg at launch. Insert your answer correct up to at least a third decimal place. KKKKKKKK

A 10-kg projectile is fired vertically upward from the ground, with an initial velocity of 50 m/s. Determine the maximum height to which it will travel if a. atmospheric resistance is neglected; and b. atmospheric resistance is measured as Fo = (0.01v²) N [v is the speed of the projectile at any instant in m/s).

A rocket travels upward at 75 m/s. When it is 80m from the ground, the engine fails. Determine the maximum height reached by the rocket. Also determine the speed just before it hits the ground. Use g= 9.81 m/s2 .

Water is discharged into the atmosphere from the pipe at 14 m/s (Figure 1). Neglect the resistance provided by the pipe at C, and the weight of the pipe and the water within it. 100 mm B 300 mm 60 mm 150 mm A Determine the horizontal component of force that is developed at the fixed support A by the ground in order to hold the pipe in equilibriu Determine the vertical component of force that is developed at the fixed support A by the ground in order to hold the pipe in equilibrium. Determine the moment that is developed at the fixed support A by the ground in order to hold the pipe in equilibrium.

m A roller coaster car and passenger with a mass of m = 800 kg starts at point A with a speed of V₁ = 9 - S Hints: 1. For the roller coaster car to pass through safely, the normal reaction at B, NB = 0. 2. Neglect friction, the mass of the wheels and the size of the car. A VA i aa d₁ Values for the figure are given in the following table. Note the figure may not be to scale. Variable Value 18 m TE d3 9 m 12 9 m 4.5 m Using equations of motion in normal-tangential coordinates and conservation of energy, a. Determine the speed of the roller coaster car at point B, vp. b. Determine minimum height of the first hill so that the car travels around the inside loops without leaving the track, d₁. c. Determine the speed of the roller coaster car at point C, vc. d. Determine the normal reaction at point C, N. Round your final answers to 3 significant digits/figures. UB= d₁ = VC = N = m S m da m S N