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- A particle initially located at the origin has an acceleration of a=3.00jm/s2 and an initial velocity of vi=5.00im/s. Find (a) the vector position of the particle at any time t, (b) the velocity of the particle at any time t, (c) the coordinates of the particle at t = 2.00 s, and (d) the speed of the particle at t = 2.00 s.arrow_forwardQuestion 2: #63 In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is con-fined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. Tall tale, or possible?arrow_forwardA particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 7.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds) (b) Find the velocity of the particle at any time t. (c) Find the coordinates of the particle at t = 8.00 s (d) Find the speed of the particle at t = 8.00 sarrow_forward
- Suppose a rocket-propelled motorcycle is fired from rest horizontally across a canyon 1.00 km wide. (a) What minimum constant acceleration in the x-direction must beprovided by the engines so the cycle crosses safely if the opposite side is0.660 km lower than the starting point?_________ m/s2 (b) At what speed does the motorcycle land if it maintains this constanthorizontal component of acceleration? Neglect air drag, but remember thatgravity is still acting in the negative y-direction._________ m/sarrow_forwardLet the position vector (with its tail at the origin) of a moving particle be~r(t) = t^(2)ˆi − 2tˆj + (t^(2) + 2t)ˆk, where ~r(t) is measured in meters and t is measured in seconds.(a) Find the acceleration vector and the magnitude of the particle at time t.(b) Find the acceleration vector and the magnitude of the particle when it passes throughthe point (4, -4, 8).arrow_forwardWhen the velocity of the moving body is non-zero, its acceleration must be non-zero also.True or Falsearrow_forward
- 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).arrow_forwardA particle initially located at the origin has an acceleration of = 4.00ĵ m/s2 and an initial velocity of i = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 7.00 s.x = my = m(d) Find the speed of the particle at t = 7.00 s.m/sarrow_forwardA person in a rowboat is 3 km from a point P on a straight shore while his destination is 5m directly east of point P. If he is able to row 4 km per hour and walk 5 km per hour, how far from his destination must he land on the shore in order to reach his destination in the shortest possible?arrow_forward
- A particle initially located at the origin has an acceleration of = 2.00ĵ m/s2 and an initial velocity of i = 9.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds).( t î + t2 ĵ) m(b) Find the velocity of the particle at any time t.( î + t ĵ) m/s(c) Find the coordinates of the particle at t = 5.00 s.x = my = m(d) Find the speed of the particle at t = 5.00 s. m/sarrow_forwardFor an object moving in a horizontal straight line: If the acceleration a(t) is less than zero and velocity v(t) is less than zero at time t, then we can say that the object is____ A. slowing down B. speeding up C. changing direction D. moving with uniform speedarrow_forwardQuestion 2: #63 In 1780, in what is now referred to as "Brady's Leap," Captain Sam Brady of the U.S. Continental Army escaped certain death from his enemies by running horizontally off the edge of the cliff above Ohio's Cuyahoga River, which is con-fined at that spot to a gorge. He landed safely on the far side of the river. It was reported that he leapt 22 ft across while falling 20 ft. Tall tale, or possible? a. What is the minimum speed with which he'd need to run off the edge of the cliff to make it safely to the far side of the river? b. The world-record time for the 100 m dash is approximately 10 s. Given this, is it reasonable to expect Brady to be able to run fast enough to achieve Brady's leap?arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning