Additional Questions . Two Dimensional Kinematics

[1]:Along jumper leave the ground at an angle of 20to the horizontal and at a speed of 11m/s

[2]: A stone is thrown from the top of a building upward at an angle of 30.0 ° to the horizontal with an initial speed of 20.0 m/s, as shown in Figure. If the height of the building is 45.0 m,

[3]: A ball from a tower of height 30 m is projected down at an angle of 30° from the horizontal with a speed of 10 m/s. How long does it take the ball to reach the ground. (Consider g = 10 m/s2 ) :

[4]:On a hot summer day a young girl swings on a rope above the local swimming hole. When she lets go of the rope her initial velocity is 2.25 m/s at an angle of 35.0° above the horizontal. If she is in flight for 1.60 s, how high above the water was she when she let go of the rope?

[5] A projectile is launched horizontally with an initial speed v₀ from a height y₀. Neglect aerodynamic friction.

v₀ = 3.5 m/s

[6] A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?

[7] The vector position of a particle varies in time according to the expression r =(3.00ˆi -6.00t2 ˆj ) m. (a) Find expressions for the velocity and acceleration as functions of time. (b) Determine the particle’s position and velocity at t = 1.00 s.

[8] A projectile is fired in such a way that its horizontal range is equal to three times its maximum height. What is the angle of projection?

[9] A fireworks rocket explodes at height h, the peak of its vertical trajectory. It throws out burning fragments in all directions, but all at the same speed v. Pellets of solidified metal fall to the ground without air resistance. Find the smallest angle that the final velocity of an impacting fragment makes with the horizontal.

[10] An automobile whose speed is increasing at a rate of 0.600 m/s² travels along a circular road of radius 20.0 m. When the instantaneous speed of the automobile is 4.00 m/s, find (a) the tangential acceleration

component, (b) the centripetal acceleration component, and (c) the magnitude and direction of the total acceleration.

[11] A pendulum with a cord of length r =1.00 m swings in a vertical plane . When the pendulum is in the two horizontal positions θ=90.0° and θ= 270°, its speed is 5.00 m/s. (a) Find the magnitude of the radial acceleration and tangential acceleration for these positions. (b) Draw vector diagrams to determine the direction of the total acceleration for these two positions. (c) Calculate the magnitude and direction of the total acceleration.