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- The positionr→of a particle moving in an xy plane is given byr→=(5.00t3−6.00t)i^+(2.00−2.00t4)j^withr→in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).if the marble is launched with the launch speed V_{o} but at an initial angle of , what would be the expression of v_{0} in terms of horizontal displacement x and vertical displacement y? Hint: y = (v_{0} * sin theta) * t - 1/2 * q * t ^ 2 and replace t using x = (v_{0} * cos theta) t .You are given a velocity with magnitude 60 m/s , with an x-component of -22 m/s what are two possibilities for its y-component
- Figure OQ3.3 shows a birds-eye view of a car going around a highway curve. As the car moves from point 1 to point 2, its speed doubles. Which of the vectors (a) through (e) shows the direction of the cars average acceleration between these two points?An ice skater is gliding along at 2.1 m/s , when she undergoes an acceleration of magnitude 1.4 m/s2 for 3.0 s. After that she's moving at 6.3 m/s . Find the angle between her acceleration vector and her initial velocity vector.An object is projected upward from ground level at an angle (Theta) and the air resistance is negligible. If the initial velocity, v0, of the object is given in ft/sec and time t is measured in seconds, then the formulas for the object's height h and the horizontal distance traveled (the range) d after t seconds into flight are as follows. h= V0 t sin (Theta) - 16t2 d = tv0 cos (Theta) If (Theta) = 30 (Degrees) and the initial velocity is 140 ft/sec what is the following? (a) The object's maximum height. (b) The object's range.
- The pilot of an aircraft flies due north relative to the ground in a wind blowing 80 km/h toward the east. If his speed relative to the air is 410 km/h, what is the magnitude of the velocity of his airplane relative to the ground? State the answer to the nearest tenth of the km/h.A rock is thrown horizontally with a velocity of 27 m/s at 30 degrees. How long does the rock take as it reaches the ground if the measured distance is only 1.5 meters? Find first the horizontal component.A projectile is fired at an angle above the horizontal at a location where g = 9.8 m/s2. The initial x and y components of its velocity are 86.6 m/s and 50 m/s respectively. At what angle was the projectile fired above the horizontal?
- The position r→ of a particle moving in an xy plane is given by r→=(3.00t^3−7.00t)i^+(6.00−2.00t^4)j^ with r→ in meters and t in seconds. In unit-vector notation, calculate(a)r→, (b)v→, and (c)a→ for t = 2.00 s. (d) What is the angle between the positive direction of the x axis and a line tangent to the particle's path at t = 2.00 s? Give your answer in the range of (-180o; 180o).A train at a constant 60.0 km/h moves east for 40.0 min, then in a direction 50.0° east of due north for 20.0 min, and then west for 50.0 min.What are the (a) magnitude and (b) angle of its average velocity during this trip?A stone is catapulted at time t 0, with an initial velocity of magnitude 20.0 m/s and at an angle of 40.0° above the horizontal. What are the magnitudes of the (a) horizontal and (b) vertical components of its displacement from the catapult site at t =1.10 s? Repeat for the (c) horizontal and (d) vertical components at t =1.80 s, and for the (e) horizontal and (f) vertical components at t = 5.00 s.