In the figure, particle A moves along the line y = 34 m with a constant velocity v of magnitude 3.4 m/s and parallel to the x axis. At the instant particle A passes the y axis, particle B leaves the origin with zero initial speed and constant acceleration a of magnitude 0.5 m/s?. What angle e between a and the positive direction of the y axis would result in a collision?

Johnny comes across a river that is 252 meters wide. He sees that the water flows eastward with a uniform velocity of 1.10m/s. Johnny sees his friend Sarah start her boat at point A on the south bank and start to cross the river to point B which is on the other side. Suppose the trip takes 3 minutes. Figure out the velocity of sarah's boat with respect to a) Johnny who is stationary on the ground b) A floating goose that's moving with the water. N B W-E S Vriver = 1.1 m/s A 252 m

Consider two particles A and B moving with constant acceleration on a plane. At time t=0, particle A is at the origin (x=0,y%=D0) and is moving with initial velocity VA = (30 m/s)î + (40 m/s)j. At time t=0, particle B is at the point (x=20 m, y=0) and is moving with initial velocity Vg = (50 m/s)j. Both particles have the same acceleration å = (-10 m/s²)ĵ 14. What is the magnitude of the average velocity of the particle A during the time interval from t=0 to t=2 s?

A particle's position is given by  z(t) = −(7.30 m/s2)t2  for  t ≥ 0.  (Express your answer in vector form.) (a) Find the particle's velocity at  t = 2.50 s  and  t = 3.25 s. (b) What is the particle's average velocity during the time interval from  t = 2.50 s  to  t = 3.25 s?

A particle confined to the xy-plane is in uniform circular motion around the origin. The x- and y-coordinates of the particle vary with time as follows: x(t) = r sin(cot) y(t) = r cos(cot). where >= 2.60 m and c = 2.15 s-¹. What are the x- and y-components of the particle's acceleration at an instant when x = 1.00 m and y = 2.40 m. Give your answers by entering numbers into the empty boxes below. ax || || X x² ms ms-2.

The 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.

A particle is moving on xy plane, with x=15sin(2t), and y = 20cos(2t) Find the magnitude of the velocity as a function of time

A projectile is fired from ground level at time t=0, at an angle θ with respect to the horizontal. It has an initial speed v0. In this problem we are assuming that the ground is level. Find the time tH it takes the projectile to reach its maximum height H.  Find tR, the time at which the projectile hits the ground after having traveled through a horizontal distance R. Find H, the maximum height attained by the projectile. Find the total distance R (often called the range) traveled in the x direction; see the figure in the problem introduction.

On a spacecraft, two engines are turned on for 908 s at a moment when the velocity of the craft has x and y components of v0x = 5150 m/s and v0y = 6290 m/s. While the engines are firing, the craft undergoes a displacement that has components of x = 2.85 x 106 m and y = 4.72 x 106 m. Find the (a) x and (b) y components of the craft's acceleration

When a chronometer begins with a time of zero seconds, matching soccer balls have a horizontal separation, d=6.28m. The ball on the left is released from the ground with an initial velocity of magnitude v0 directed toward the other soccer ball. The ball on the right has an initial height h1=3.17m and is momentarily at rest. A short time later, the matching soccer balls collide at the collision point, C, at a height h2-1.69m above the ground, as indicated on the diagram. Ignore the finite size of the balls, and additionally ignore any air resistance. (Dimensions are not to scale.) Part (a)  Given the numeric values in the problem statement, tabulate the elapsed time, in seconds, at which the matching soccer balls collide.  Part (b)  Given the numeric values in the problem statement, tabulate the magnitude, in meters per second, of the initial velocity of the soccer ball on the left.