A small rocket is launched vertically from rest and it accelerates uniformly at 26 m/s² for a period of 13 s, at which point all of its fuel is used. The rocket then continues to travel freely in the vertical direction until it eventually reaches its maximum altitude, after which it falls to earth. Working to 4 significant figures, calculate for the rocket: (a) Its velocity at the instant when all of its fuel is used. m/s (b) Its altitude at the instant when all of its fuel is used. m (c) (i) The time taken for the rocket to slow from the point it runs out of fuel until it reaches maximum altitude. S (ii) The total time taken to reach its maximum altitude S (d) The maximum altitude reached m (e) Its velocity at the instant just prior to impact with the ground. m/s

Modern roller coasters have vertical loops like the one shown in the figure. The radius of curvature is smaller at the top than on the sides so that the downward centripetal acceleration at the top will be greater than the acceleration due to gravity, keeping the passengers pressed firmly into their seats. Part (a)  What is the speed of the roller coaster, in meters per second, at the top of the loop if the radius of curvature there is 15 m and the downward acceleration of the car is 1.3g? Note that g here is the acceleration due to gravity.  Part (b)  The beginning of this roller coaster is at the top of a high hill. If it started from rest at the top of this hill, how high, in meters, above the top of the loop is this initial starting point? You may assume there is no friction anywhere on the track.  Part (c)  If it actually starts 3.5 m higher than your answer to the previous part (yet still reaches the top of the loop with the same velocity), how much energy, in joules, did it lose…

Q1 A balloon is rising vertically above a level, straight road at a constant rate of 2 ft sec. Just when the balloon is 60 ft above the ground, a bicycle moving at a constant rate of 17 ft sec passes under it. How fast is the distance s(t) between the bicycle and balloon increasing 3 sec later?

A car accelerates uniformly from rest and reaches a speed of 28.0 m/s in 8.00 s. If the radius of a tire is 30 cm, find thenumber of revolutions the tire makes during this motion, assuming that no slipping occurs.

Q4) A grasshopper leaps into the air from the edge of a vertical eliff, as shown in Figure. Use information from the figure to find (a) The initial speed of the grasshopper and (b) The height of the cliff. 6.74 cm 50.0 Not to scale 1,06 B

A ceiling fan is moving at a constant rotation rate and makes one revolution in 1.3 s. The distance from the fan's center to the outermost tip of a blade is 1 m. A fly F is resting right at the tip. What is the fly's acceleration?

Q.2: A train travels at v = 20(1 – e-3t) where t in seconds and v in ft/s; (a):the distance after 2 seconds is: Q2/(b):the acceleration after 2 seconds is:

1) Most of us rode bikes a kid. Did you ever accidentally apply the front brake while riding down a hill and flip over your handlebars? Let's analyze the level of deceleration needed to cause this to happen (at this instant the normal force of the rear tire is zero). Assume the rider is moving down a hill at a constant velocity and att = 0, the rider squeezes the brakes and begins to decelerate. This action results in a force that points in the bi direction and passes through the contact points between the tires and the pavement. Be sure to include your FBD, IRD, and transformation array. b2 30 in. FB 13 in. 23 in.

Consider a rocket at take off. Assume that the rocket is moving vertically for the time in question here. The acceleration (in m/s²) as a function of time is given by a(t) = 1.5 + 0.47 t + 0.10 t² (with t in seconds and the take off at t=0). What is the speed of the rocket at 16 s (in m/s).

A 150-m-wide river flows due east at a uniform speed of 2.0 m/s. A boat with a speed of 6.0 m/s relative to the water leaves the south bank pointed in a direction 30° west of north. (a) Draw the vectors triangle using scale 1.0 cm : 1.0 m/s and label the corresponding relative velocities. (b) Determine the magnitude of the boat's velocity relative to the ground. (c) Determine the direction of the boat's velocity relative to the ground. (d) Find the time for the boat to cross the river. SS