A Boeing 777, initially at rest, undergoes a constant acceleration of 2.3 m/s^2

Question

A Boeing 777, initially at rest, undergoes a constant acceleration of 2.3 m/s^2 down the runaway for 34s before it lifts off. a) How far does it travel down the runway before taking off? b) What is the speed of the aircraft as it lifts off? At an amusement park, free fall riders seated in a padded gondola are taken to the top of a 10 story tower then dropped 30m down a vertical track that curves near the bottom, where the gondola stop. a) How long does it take to fall the 30m from top slows to a to bottom? b) What maximum speed is reached? A ball is thrown with an initial velocity of 50 m/s at an angle of 60 degree above the horizontal. Find: a) Maximum height (apex). b) Time to top (apex). c) Total time of flight. d) Down range of the ball. e) Velocity of the ball upon striking ground. (Remember, velocity is a vector) f) Position and velocity of the ball at t = 4 seconds. A horizontal force of 100N is applied to a box of mass 20kg resting on a wooden table. Does the box slide if the coefficient of friction of the box on the table is 0.40? If the box moves, find its acceleration. An industrial grinding wheel with a 25.4cm diameter spins at a rate 1910 rpm. What is the linear speed of a point on the rim? At an amusement park the 'Wheelie' carries passengers in a circular path with radius 7.7m. The ride makes a complete rotation every 4.0s. (a) What is a passenger's angular velocity and (b) What acceleration does a passenger experience? How much work is required to extend an exercise spring by 45cm if the spring constant k has the value 310 N/m? b) What force is required to extend the spring by 45cm? A student knocks a plant off the window sill, where it falls from rest to the ground 5.27m below. a) Use the principle of conservation of energy to determine its speed just before it strikes the ground: b) Use kinematics to check your work. Given I_disk = 1/2 mR^2 and I_hoop = mR^2, which will have a greater speed along an inclined plane and why? Calculate the period of oscillation for a pendulum of length 1m. What is the gravitational force between two 60kg adults, separated by 1m. You are standing on a frictionless surface and catch a 0.400-kg ball thrown by a friend. The ball's horizontal velocity was 15.0 m/s and your mass is 80 kg. Your speed (and that of the ball) after catching the ball is____.

Explanation / Answer

1. (a) d = ut + a t^2 /2

d = 0 + (2.3 x 34^2 /2) = 1329.4 m

(b) v = v0+ at = 0 + (2.3 x 34) = 78.2 m/s

2. (a) y = v0y t + ay t^2 /2

- 30 = 0 - 9.8 t^2 /2

t = 2.47 sec

(b) v= v0 + a t = 0 + (-9.8 x 2.47) = - 24.25 m/s

maximum speed = 24.25 m/s downward

3. (A) H = v0^2 (sin(theta))^2 /2g

= 50^2 (sin60)^2 / 2x9.8

= 95.7 m/

(b) t = v0 sin(theta) / g

= 4.42 sec

(c) time of flight = 2t = 8.84 sec

(d) R = v0^2 sin(2 theta) / g

= 50^2 sin120 / 9.8

= 220.92 m

(e) 50 m/s 60 deg below the horizontally

(f) Position :

x = (50 cos60)(4) = 100 m

y = (50 sin60)(4) - (9.8 x 4^2 / 2) = 94.8 m

velocity:

vx = 50 cos60 = 25 m/s

vy = 50 sin60 - (9.8 x4) = 4.10 m/s

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