A series of long problems involving Acceleration, Gravity, Speed, Distance

1. Oct 2, 2010

asz304

Hi, I need help with most of these problems. I am not expecting you to answers my questions, instead I would like to have some tips/hints on the problems. Thank you

FORMULAS TO USE:

Xf = Xi + 1/2(Vxf + Vxi)t
Vxf = Vxi + AxT
Xf = Xi + VxiT + 1/2AxT^2
Vxf^2 = Vxi + 2Ax(Xf - Xi)

Vyf = Vyi + GxT
Yf = Yi + 1/2 (Vyf + Vyi)T
Yf = Yi + VxiT + 1/2 GxT^2
Vyf^2 = Vyi + 2Gx( Yf - Yi )

13. [2pt]
A truck is stopped for a red light at Ridge Road on Higgins line. At the instant the light turns green, the truck pulls away with a constant acceleration of 2.1 m/s2. A cyclist approaching the truck with a constant velocity of 12.0 m/s is 7.90 m behind the truck when the light turns green. What is the elapsed time from the changing of the light to when the cyclist passes the truck?What is the elapsed time from the changing of the light to when the truck repasses the cyclist? How far has the truck travelled from the stoplight when it repasses the cyclist?

19. [2pt]
To save fuel, some truck drivers try to maintain a constant speed when possible. A truck traveling at 87.0 km/hr approaches a car stopped at the red light. When the truck is 113.5 meters from the car the light turns green and the car immediately begins to accelerate at 2.60 m/s2 to a final speed of 100.0 km/hr. How close does the truck come to the car assuming the truck does not slow down?How far from the stop light has the car travelled when the truck reaches its closest distance?

21
The location of a particle (in m) is given by its x, y and z coordinates as function of the time (in s) as:

x = -19+27t and y = -27+21t+11t2 and z = 25-11t-9t2

Calculate the magnitude of the displacement from t = -7.00 s to t = -2.00 s.Calculate the magnitude of the particle's average velocity between t = -7.00 s and t = -2.00 s.Calculate the z-component of the instantaneous velocity at t = 1.00 s?What is the magnitude of the object's acceleration at t = -7.00 s?

22. [3pt]
A catapult on a cliff launches a large round rock towards a ship on
the ocean below. The rock leaves the catapult from a height H of 31.0 m above sea level, directed at an angle above the horizontal with an unknown speed v0. The projectile remains in flight for 6.00 seconds and travels a horizontal distance D of 170 m. Assuming that air friction can be neglected, calculate the value of the angle (in degrees). Calculate the speed at which the rock is launched.

31. [2pt]
A stone thrown horizontally from a height of 5.82 m hits the ground at a distance of 12.30 m. Calculate the initial speed of the stone. Neglect air resistance.Calculate the speed of the stone as it hits the ground. Neglect air resistance.

36. [3pt]
A toy car is driven horizontally off of a level platform at the top of a ramp as shown. The velocity of the car just as it leaves the ramp is 5.88 m/s. The angle of the ramp with respect to the horizontal direction, theta, is 39.4 °. How far does the car travel HORIZONTALLY before landing on the ramp?How long is the car in the air?What is the magnitude of the car's velocity just before it lands on the ramp?

37. [2pt]
As a locomotive rounds a circular curve of radius 2.40 km, its speed is increasing at a rate of 0.460 m/s2. An instrument in the cab (an accelerometer) indicates that the magnitude of the locomotive's total acceleration at a particular instant is 0.700 m/s2. What is the locomotive's speed at that instant?

38. [2pt]
A spacecraft moves in a circular orbit with a speed of 7.60 km/s with a period of 95.1 min. What is the radius of the spacecraft's orbit? What is the radial acceleration of the satellite?

39. [2pt]
In order to begin its re-entry, the spacecraft engines are fired to provide an acceleration of 6.90 m/s2 in a direction opposite to its velocity. What is the magnitude of the spacecraft's total acceleration just after the engines begin to fire.

45. [1pt]
The compass in a plane indicates that the plane is heading west; its air speed indicator reads 201 km/hr. There is a steady wind blowing from the south with a speed of 59.0 km/hr. What is the speed of the plane with respect to the ground?

54.
A wind is blowing directly from east to west. The pilot of a small plane finds that if he points the nose of the plane 27.9 ° north of east, his velocity with respect to the ground is in the direction 53.9 ° north of east. The speed of the plane with respect to the air is 127 m/s. Taking North to be the y-direction and East to be the x-direction, what is the y-component of plane's velocity with respect to the ground? What is the magnitude of the plane's velocity with respect to the ground?

2. Oct 2, 2010

fss

Where are your attempts at solutions to these problems? If you haven't attempted, why can you not even start them?