![]() ![]() The wall is 22.0m from the release point of the ball. You throw a ball with a speed of 25.0 m s at an angle of 40.0 0 above the horizontal directly toward a wall, as shown in Fig. 1(b) we let θ be the angle below the horizontal at which the velocity vector is pointing, we see thatĪt the time of impact, the velocity of the mug was directed at 50.9 0 below the horizontal. So at the time of impact, the speed of the mug was Substitute into our expressions for v x and v y: (b) We want to find the components of the mug’s velocity at the time of impact, that is, at t = 0. Which tells us that the initial speed of the mug was v 0 = 3.34 m/s. 419 s we know that the x coordinate was equal to 1.40 m. To find v 0x we consider the x equation of motion x 0 = 0 and a x = 0, so we haveĪt t = 0. This is the time t at which y = −0.860m (recall how we chose the coordinates!), and we will need the y equation of motion for this since v 0y = 0 and a y = −g, we get: We might begin by finding the time t at which the mug hit the floor. (In fact, that’s what we’re trying to figure out!) (This is because its velocity was horizontal all the time it was sliding on the counter.) So we know that v 0y = 0 but we don’t know the value of v 0x. So the mug’s initial coordinates for its flight are x 0 = 0, y 0 = 0.Īt the very beginning of its motion through the air, the velocity of the mug is horizontal. We choose the origin of our xy coordinate system as being at the point where the mug leaves the counter. ![]() (a) The motion of the beer mug is shown in Fig.1(a). If the height of the counter is 0.860 m, (a) with what speed did the mug leave the counter and (b) what was the direction of the mug’s velocity just before it hit the floor? The bartender does not see the mug, which slides off the counter and strikes the floor 1.40m from the base of the counter. In a local bar, a customer slides an empty beer mug on the counter for a refill. The muzzle velocity of the bullet is 480 m/s. Since this is the time of impact with the target, the time of flight of the bullet is t = 6.2×10 −2 s. We don’t know the time of flight but we do know that when x has the value 30 m then y has the value −1.9×10 −2 m. What else do we know? The gun is fired horizontally so that v 0y = 0, but we don’t know v 0x. ![]() 3.1, where the origin is placed at the tip of the gun. I will use the coordinate system indicated in Fig. (a) What is the bullet’s time of flight? (b) What is the muzzle velocity? The bullet hits the target 1.9 cm below the aiming point. Problem 7 A projectile starting from ground hits a target on the ground located at a distance of 1000 meters after 40 seconds.Soal #1A rifle is aimed horizontally at a target 30 m away. Ī) What is the initial velocity V 0 of the ball if its kinetic energy is 22 Joules when its height is maximum?ī) What is the maximum height reached by the ball Problem 6 A ball of 600 grams is kicked at an angle of 35° with the ground with an initial velocity V 0. Problem 5 A ball kicked from ground level at an initial velocity of 60 m/s and an angle θ with ground reaches a horizontal distance of 200 meters. Problem 4 A ball is kicked at an angle of 35° with the ground.Ī) What should be the initial velocity of the ball so that it hits a target that is 30 meters away at a height of 1.8 meters?ī) What is the time for the ball to reach the target? Problem 3 A projectile is to be launched at an angle of 30° so that it falls beyond the pond of length 20 meters as shown in the figure.Ī) What is the range of values of the initial velocity so that the projectile falls between points M and N? The projectile hits the incline plane at point M.Ī) Find the time it takes for the projectile to hit the incline plane. Problem 2 A projectile is launched from point O at an angle of 22° with an initial velocity of 15 m/s up an incline plane that makes an angle of 10° with the horizontal. Problem 1 An object is launched at a velocity of 20 m/s in a direction making an angle of 25° upward with the horizontal.Ī) What is the maximum height reached by the object?ī) What is the total flight time (between launch and touching the ground) of the object?Ĭ) What is the horizontal range (maximum x above ground) of the object?ĭ) What is the magnitude of the velocity of the object just before it hits the ground? An interactive html 5 applet may be used to better understand the projectile equations. These problems may be better understood when Projectile problems are presented along with detailed solutions. ![]()
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