If the particle travels the plane then . . .? down Answer: The component of in the (g sin) is positive. See example 2008 (b) g x-direction plane of projection is vertical and contains the line of greatest “The slope.” This line appears in most of these questions you need it. Put a line through it. – don’t It just means that the projectile goes up the hill but it how you answer the question. straight doesn’t affect The particle strikes the inclined plane at right angles {We usually do a few of these in Fifth Year as an introduction to Inclined Plane questions but that’s usually as far as we go with Projectiles in Fifth Year} To find the range (if the particle strikes the inclined plane at right angles) We would normally sub our expression for into the equation which usually involves some complicated t Sx algebra and possibly some trigonometric substitutions). Nice alternative: Just use v2 = u2 + 2as in the direction x vx = 0 So it reduces to ux2 = - 2axs s = ux2 /-2ax See next question for an example 1982 A particle is projected with a speed of 10 m/s at an angle to the horizontal up a plane inclined at 300 to the α horizontal. If the particle strikes the plane at right angles, show that the time of flight can be represented by the two expressions and . Hence deduce a value for tan 30). (α – the range of the particle along the plane. 2002 (b) A particle is projected with velocity u m/s at an angle to the horizontal, up a plane inclined at an angle θ β to the horizontal. (The plane of projection is vertical and contains the line of greatest slope).
If the particle travels down the plane then . . .? Answer: The component of g in the x-direction (g sin) is positive. See example 2008 (b) “The plane of projection is vertical and contains the line of greatest slope.” This line appears in most of these questions – you don’t need it. Put a line through it. It just means that the projectile goes straight up the hill but it doesn’t affect how you answer the question. The particle strikes the inclined plane at right angles {We usually do a few of these in Fifth Year as an introduction to Inclined Plane questions but that’s usually as far as we go with Projectiles in Fifth Year} To find the range (if the particle strikes the inclined plane at right angles) We would normally sub our expression for t into the Sx equation which usually involves some complicated algebra and possibly some trigonometric substitutions). Nice alternative: Just use v2 = u2 + 2as in the x direction vx = 0 So it reduces to ux2 = - 2axs s = ux2 /-2ax See next question for an example 1982 A particle is projected with a speed of 10 m/s at an angle α to the horizontal up a plane inclined at 300 to the horizontal. If the particle strikes the plane at right angles, show that the time of flight can be represented by the two expressions and . Hence deduce a value for tan (α – 30). the range of the particle along the plane. 2002 (b) A particle is projected with velocity u m/s at an angle θ to the horizontal, up a plane inclined at an angle β to the horizontal. (The plane of projection is vertical and contains the line of greatest slope).