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The acceleration due to gravity of a particle falling toward the earth is
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Vector Mechanics For Engineers
- The motion of a particle is defined by the function x = at3 - bt2 - ct + d where x is in centimeters and t is in seconds When is the particle at rest if a = 1.3, b = 3.5, c = 8.3, and d = 5.2?arrow_forwardThe range R, or the maximum horizontal distance, of a projectile on level ground launched at an angle 8 above the horizontal with initial speed v is given by R = ² sin 20 Show the 9 derivation of this formula.arrow_forwardTwo airplanes are performing at an air show. Plane B enters the circular path (r =140 meters) at point O with a velocity of (vB)o = 45 m, which is increasing at a rate of 0.004s2 m, where "s" is the arc length measured from point O in meters. Plane A is travelling along a straight inclined path (0= 36°) and has a constant velocity of va = 122 m. Determine the magnitude of the tangential acceleration vector of plane B (in ) when it has travelled 30° around the circular path. A 30°( y (VB)o В - Xarrow_forward
- The resistance force due to water acting on a boat is proportional to its instantaneous speed, and is such that at 30 feet per second it is 90 pounds. If the boat and its only passenger together weigh 448 pounds and the motor can exert a constant force of 540 pounds in the direction of motion, determine the speed v (t) of the boat, in ft / s, depending on time t, in seconds , assuming that the boat starts from rest. Consider the acceleration of gravity as g = 32 ft / s²arrow_forwardHow long will it take for a car, starting from rest, to acquire a speed of60 mi/hr if its acceleration is 12 ft/sec 2?arrow_forwardTwo airplanes are performing at an air show. Plane B enters the circular path (r =105 meters) at point O with a velocity of (vB)o = 48 m, which is increasing at a rate of 0.007s2 m. where "s" is the arc length measured from point O in meters. Plane A is travelling along a straight inclined path (0= 38°) and has a constant velocity of va = 132 m. Determine the magnitude of the velocity vector of plane B (in m) when it has travelled 30° around the circular path. A 30 y В -arrow_forward
- The force acting on the particle is equal to the rate of change of of the particle. Acceleration Velocity Linear momentum Impulsearrow_forwardThe basketball passed through the hoop even though it barely cleared the hands of the player B who attempted to block it. Suppose that s = 5 ft. Neglect the size of the ball. 10 ft 25 n Part A Determine the magnitude v of its initial velocity. Express your answer to three significant figures and include the appropriate units. VA= Part B Determine the height h of the ball when it passes over player B. Express your answer to three significant figures and include the appropriate units. h =arrow_forwardAfter being hit by the club at A, the golf ball has an initial velocity of vA= 28 m directed at the angle of 0 = 33°. The angle of inclination of the ground is a = 13°. If it takes t = 10 seconds for the golf ball to hit the ground at point B, what is the magnitude of the velocity vector (in m) of the golf ball at point B. Consider g =10 m В VA d Aarrow_forward
- A particle is initially at rest and given an acceleration a = 6t² m/s² where t is in seconds. What is its velocity at t = 2 s? O 16 m/s O 32 m/s O24 m/s 48 m/sarrow_forwardAs part of an obstacle course, an athlete must kick a soccer ball into al meter wide and 10 meter deep pit such that the ball hits a target at the bottom of the pit. In practice, a dynamics student that is participating in the race kicks the soccer ball such that the soccer ball will bounce off the far wall of the pit 5 meters below the surface and head towards the target. If the velocity of the ball before striking the wall at point at point A is vA=3.21- 10j , determine the t-component of the ball velocity vector (in m) after striking the wall. The size of the ball and the target are negligible relative to the dimensions of the pit, the gravity acceleration must be considered as g = 10 and the coefficient of restitution at point A is e =0.55. 5 m 10m Im 目arrow_forwardA particle is projected vertically upward, under gravity, with a speed of 48 ft/sec. One second later, another particle is fired upward from the same point. Find the initial speed of this particle in order that the two particles will collide when the first particle has reached its highest point (take g = 32 ft/sec²).arrow_forward
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