A ball has an initial velocity of 1.50 m/s along the x-axis. Starting at t,-0, the ball receives an acceleration of 2.8 m/s in the y-direction. Find the following: a) What is the position and distance from the starting point of the ball 3.0 seconds after g? b) What is the velocity in both magnitude and direction of the ball at 3.0 seconds? c) Provide a plot of position vs time from t,=0 to t=3.0seconds.
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- A particle moves down a horizontal route that begins 5 feet to the right of a specific point P with an initial velocity of 4 feet per second. Another particle is going along the same route, beginning 3 feet to the left of P with an initial velocity of 8 feet per second. Consider that the accelerations of the two particles are a1(t) = 2t 3 and a2(t) = 2t 5, respectively. Will the particles collide? Justify your responseFor projectile motion problems, the horizontal and vertical components of the motion of a projectile can be analyzed separately. Which of the following is TRUE about the horizontal component of its motion?a. The horizontal component of the acceleration is constant and is equal to -9.81 m/s^2b. The motion is uniformc. The horizontal component of the velocity varies with positiond. The motion is uniformly acceleratedThe position of a particle along the positive x-axis is given by the following function r = 1t3 +14t2 +4, find the speed of the particle at time t=17, where t is in seconds and r is in cm. Recall that the velocity can be found by taking the derivative of the position vector. Express your answer in cm/s.
- The record distance in the sport of throwing cowpats is 81.1 m.m. This record toss was set by Steve Urner of the United States in 1981 . Assuming the initial launch angle was 45∘45∘ and neglecting air resistance, determine (a) the initial speed of the projectile and (b) the total time the projectile was in flight.In the two-dimensional motion, what is the magnitude of the y component of the velocity of the projectile when it is at its apex of trajectory? Select one: a. Velocity is equal to the initial velocity b. Velocity is 9.81 m/s c. Velocity is equal to the x component d. Undetermined e. Velocity is 0 m/sTwo stones are thrown vertically up with the initial velocity v0, second stone with a time delay t0 with respect to the first one. At which time after the beginning of the motion the two stones will collide? Is this scenario possible for any v0 and t0? What are the limitations?
- The record distance in the sport of throwing cowpats is 81.1 m. This record toss was set by Steve Urner of the United States in 1981. Assuming the initial launch angle was 45° and neglecting air resistance, determine the following: (a) the initial speed of the projectile and (b) the total time the projectile was in flight.A model rocket is fired from the roof of a 50 ft. tall building as shown in the figure below. The height of the rocket is given by: y(t) = 150t - 16.1t2+ 50ft Find the following. a) The velocity v(t) = dy/dt as well as the initial velocity v0 = v(0) b) The acceleration a(t) = dv/dt c) The time required to reach the maximum height as well as the corresponding height ymaxA ball has an initial velocity of 1.50 m/s along the x-axis. Starting at t0=0, the ball receives an acceleration of 2.8 m/s2 in the y-direction. Find the following: What is the position and distance from the starting point of the ball 3.0 seconds after t0? What is the velocity in both magnitude and direction of the ball at 3.0 seconds? Provide a plot of position vs time from t0=0 to t=3.0 seconds.
- Suppose that a ball is thrown straight up in the air, and that a secondball is thrown straight upward two seconds after the first. It reaches thesame maximum height as the first ball, which is 6.00 m.a. What is the position of the first ball as a function of time, y1(t)?Take the initial height of the ball as y0 = 0.b. What is the position of the second ball as a function of time, y2(t)?Take the initial height of the ball as y0 = 0.c. Draw a y − t diagram of y1(t) and y2(t). Label the max heights, timeto max height for the first ball, and note the point corresponding to thetime and height of passing.d. When do the balls pass each other in the air? Assume the balls arebeing throw up adjacent to each other.e. At what height above y0 = 0 do the balls pass each other?f. Can you find the time of passing by just using the y − t diagram?In a particular Cartesian coordinate system, the y and z-components of the acceleration are zero and the x-component varies as given by the following function: ax(t) = 5t - 2t2 + 45e-t/F, where t is in seconds, ax is in meters per square second, and the constant F is in seconds. At t = 0, the particle was at position x = 3 m with a velocity pointing towards the positive x-axis and having magnitude 35 m/s. In the following problem you can take the constant F = 1.0 s. Find the instantaneous velocity, in meters per second, at t = 2 s. Find the position, in meters, of the particle at t = 1 s. Find the position, in meters, of the particle at t = 3 s.A skateboarder travels on a horizontal surface with an initial velocity of 4.4 m/sm/s toward the south and a constant acceleration of 2.6 m/s2m/s2 toward the east. Let the xx direction be eastward and the yy direction be northward, and let the skateboarder be at the origin at t=0t=0. 1. What is her y position at t=0.90s? Express your answer to two significant figures and include appropriate units.