Worksheet: Projection on a Uniform Slope

In this worksheet, you will practice solve problems about the motion of a projectile on an inclined plane and describing the projectile velocity, acceleration and position vectors in terms of the unit vectors i, and j parallel and perpendicular to that plane.

Q1:

An archer shot an arrow with a speed of 80 m/s at an angle of 2 0 ∘ above the horizontal. Calculate the arrow’s horizontal range π‘₯ . Also calculate its vertical height β„Ž above the launch point when it was at a distance of 46 m from the archer. Give your answers in metres correct to one decimal place. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A π‘₯ = 2 0 9 . 9 m , β„Ž = 1 4 . 9 m
  • B π‘₯ = 2 0 9 . 9 m , β„Ž = 1 1 2 . 5 m
  • C π‘₯ = 4 1 9 . 8 m , β„Ž = 1 1 2 . 5 m
  • D π‘₯ = 4 1 9 . 8 m , β„Ž = 1 4 . 9 m
  • E π‘₯ = 8 3 9 . 6 m , β„Ž = 4 2 . 3 m

Q2:

A boulder was catapulted with a speed of 14 m/s at an angle of elevation of 5 6 ∘ from point 𝑂 on horizontal ground, which is 6 m away from a castle wall that is 6 m high. Did the boulder go over the wall? Take 𝑔 = 9 . 8 / m s 2 .

  • Ayes
  • Bno

Q3:

A catapult flung a boulder from the top of a castle wall with a speed of 11 m/s at an angle πœƒ above the horizontal, where s i n πœƒ = 4 5 . The boulder landed on the ground a distance of 66 m from the wall. Calculate the time it took for the boulder to reach the ground and find the height of the castle wall. Take 𝑔 = 9 . 8 / m s 2 .

  • A 20 s, 402 m
  • B 10 s, 405.95 m
  • C 10 s, 807.95 m
  • D 10 s, 402 m
  • E 20 s, 807.95 m

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