Motion In Two Or Three Dimensions
A drone moves so that its position is given by x(t) = 4t² and y(t) = 3t³, where x and y are in metres and t is in seconds. What is the magnitude of the drone’s velocity at t = 1.0 s?
Which statement correctly describes why the x- and y-components of a particle’s motion can be analysed independently?
A stone is launched horizontally at 12 m/s from the edge of a 45 m tall cliff. How long does it take to reach the ground? Use g = 10 m/s².
A projectile is launched at 25 m/s at 53° above the horizontal from level ground. What is the horizontal range of the projectile? Use g = 10 m/s² and sin 106° ≈ 0.96.
A particle has position x(t) = 2t and y(t) = 8t − 5t². At what time does the particle reach its maximum height?
An object is launched at speed v₀ at angle θ above the horizontal from level ground. Which expression gives the maximum height reached by the object?
A rescue helicopter flies horizontally at constant velocity at an altitude of 80 m. A supply package is released from the helicopter. Which statement correctly describes the package’s horizontal velocity immediately after release, assuming air resistance is negligible?
A ball is kicked from ground level at 20 m/s at an angle of 45° above the horizontal. What is the speed of the ball at the highest point of its trajectory? Use g = 10 m/s².
Two cannons are positioned at the edge of a 200 m cliff. Cannon A fires a ball horizontally at 50 m/s. Cannon B fires a ball horizontally at 100 m/s. Both fire simultaneously. Which ball strikes the ground first?
A particle moves with position given by x(t) = 6t − t² and y(t) = 4t. What is the direction of the particle’s velocity relative to the positive x-axis at t = 2.0 s?
A tennis ball is served horizontally from a height of 2.5 m above the ground at 30 m/s. How far from the server does the ball land? Use g = 10 m/s².
A particle has position x(t) = t³ and y(t) = 4t². What is the magnitude of the particle’s acceleration at t = 1.0 s?
A spacecraft in deep space fires two perpendicular thrusters simultaneously. Thruster X provides a constant acceleration of 3.0 m/s² along the x-axis, and Thruster Y provides a constant acceleration of 4.0 m/s² along the y-axis. The spacecraft starts from rest. What is the speed of the spacecraft after 10 s?
A football is kicked at 18 m/s at 30° above the horizontal from ground level. Calculate the vertical component of velocity 1.5 s after the kick. Use g = 10 m/s².
A stunt driver launches a car horizontally off a ramp at the edge of a canyon. The car lands on the opposite side, which is at the same elevation as the ramp, 50 m away, after 2.0 s of flight. A physicist claims the car must have been launched at 25 m/s. Is this claim consistent with the given data, and what additional physical concern arises?
A projectile is launched from ground level at speed v₀ at angle θ. Which expression correctly gives the total time of flight for a symmetric trajectory (landing at launch height)?
A ball is launched at 30 m/s at 60° above the horizontal from ground level. Calculate the horizontal range of the ball. Use g = 10 m/s².
A particle moves with x(t) = 10t and y(t) = 20t − 5t². At what time does the direction of the velocity vector make a 45° angle below the positive x-axis?
During a physics demonstration, a teacher drops ball A from a height of 1.25 m at the exact same instant that ball B is launched horizontally at 8 m/s from the same height. A student predicts that ball B will land after ball A because “it has farther to travel along its curved path.” Evaluate the student’s prediction.