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Lesson Worksheet: Projectile Motion Formulae Mathematics

In this worksheet, we will practice deriving formulae for projectile motion and using them in problems.

Q1:

A projectile is launched from a flat horizontal plane at an angle of πœƒ from the horizontal. Its initial velocity is π‘ˆ m/s, its acceleration due to gravity is 𝑔 m/s2, and no other forces act upon it during its flight. Given that its time of flight is 𝑇=π‘Žπ‘ˆπœƒπ‘”οŒΏsin s, find the value of the constant π‘Ž.

  • A2
  • B1
  • C4
  • D14
  • E12

Q2:

A projectile is launched from a flat horizontal plane at an angle of πœƒ from the horizontal. Its initial velocity is π‘ˆ mβ‹…sβˆ’1, its acceleration due to gravity is 𝑔 mβ‹…sβˆ’2, and no other forces act upon it during its flight. Given that its range on the horizontal plane is 𝑅=π‘ˆπ‘πœƒπ‘”οŒΊsinm, find the value of the constants π‘Ž and 𝑏.

  • Aπ‘Ž=2, 𝑏=2
  • Bπ‘Ž=1, 𝑏=12
  • Cπ‘Ž=1, 𝑏=1
  • Dπ‘Ž=2, 𝑏=1
  • Eπ‘Ž=1, 𝑏=2

Q3:

A projectile is launched from a flat horizontal plane at an angle of πœƒ from the horizontal. Its initial velocity is π‘ˆ msβˆ’1, its acceleration due to gravity is 𝑔 msβˆ’2, and no other forces act upon it during its flight. Given that its greatest height is β„Ž=π‘Žπ‘ˆπ‘πœƒπ‘π‘”οŠ¨οŠ¨sinm, find the value of the constants π‘Ž, 𝑏, and 𝑐.

  • Aπ‘Ž=2, 𝑏=1, 𝑐=2
  • Bπ‘Ž=1, 𝑏=1, 𝑐=2
  • Cπ‘Ž=1, 𝑏=2, 𝑐=1
  • Dπ‘Ž=2, 𝑏=1, 𝑐=1
  • Eπ‘Ž=1, 𝑏=2, 𝑐=2

Q4:

A projectile is launched from a flat horizontal plane at an angle of πœƒ from the horizontal. Its initial velocity is π‘ˆ msβˆ’1, its acceleration due to gravity is 𝑔 msβˆ’1, and no other forces act upon it during its flight. Derive an equation relating its vertical displacement 𝑦 to its horizontal displacement π‘₯ at any given time.

  • A𝑦=π‘₯πœƒβˆ’π‘”π‘₯ο€Ή1+πœƒο…2π‘ˆsincos
  • B𝑦=π‘₯πœƒβˆ’2𝑔π‘₯ο€Ή1+πœƒο…π‘ˆtantan
  • C𝑦=π‘₯πœƒβˆ’π‘”π‘₯ο€Ή1+πœƒο…2π‘ˆtantan
  • D𝑦=π‘₯πœƒβˆ’π‘”π‘₯ο€Ί1+πœƒο†2π‘ˆcossin
  • E𝑦=π‘₯πœƒβˆ’2𝑔π‘₯ο€Ί1+πœƒο†π‘ˆsinsin

Q5:

A particle is projected from a horizontal plane at an angle of 47∘ from the horizontal. After 15 seconds, the particle hits the ground. Find the starting velocity of the particle, taking 𝑔=9.8/ms and giving your answer to 1 decimal place.

Q6:

A projectile is launched from a flat horizontal plane at an angle of πœƒ from the horizontal. Its initial velocity is π‘ˆ m/s, its acceleration due to gravity is 𝑔 m/s2, and no other forces act upon it during its flight. Given that its range on the horizontal plane is 𝑅 m, find the value of πœƒ that maximizes 𝑅.

  • Aπœƒ=45∘
  • Bπœƒ=0∘
  • Cπœƒ=30∘
  • Dπœƒ=90∘
  • Eπœƒ=60∘

Q7:

A particle is projected from a horizontal plane at an angle of 20∘ from the horizontal. It reaches its greatest height after 2 seconds. Find the starting velocity of the particle, taking 𝑔=9.8/ms and giving your answer to 1 decimal place.

Q8:

A particle is projected from a horizontal plane at an angle of πœƒ from the horizontal and with an initial velocity of 18 m/s. The particle passes through point 𝐴 situated 15 m horizontally and 8 m vertically from the point of launch. Find the possible values of πœƒ, taking 𝑔=9.8/ms and giving your answer to 1 decimal place.

  • Aπœƒ=44.7∘ or πœƒ=76.3∘
  • Bπœƒ=39.6∘ or πœƒ=16.5∘
  • Cπœƒ=16.1∘ or πœƒ=76.3∘
  • Dπœƒ=44.3∘ or πœƒ=16.5∘
  • Eπœƒ=44.3∘ or πœƒ=73.8∘

Q9:

A rocket is launched vertically at a speed of 60 m/s from a point 𝑋. When it reaches its maximum height, a capsule is ejected horizontally from it at a speed of 40 m/s. Find the horizontal distance from 𝑋 to the capsule’s landing point, taking 𝑔=9.8/ms and giving your answer to 1 decimal place.

Q10:

A projectile is launched from a flat horizontal plane with an initial velocity of ij+3 m/s, where i and j are unit vectors in the horizontal and vertical directions. Its acceleration due to gravity is 𝑔 m/s2, and no other forces act upon it during its flight. Given that its position vector relative to the origin is π‘₯+𝑦ij with π‘₯ and 𝑦 related by 𝑦=π‘Žπ‘₯βˆ’π‘”π‘₯π‘οŠ¨, find the values of the constants π‘Ž and 𝑏.

  • Aπ‘Ž=3, 𝑏=2
  • Bπ‘Ž=3, 𝑏=3
  • Cπ‘Ž=2, 𝑏=3
  • Dπ‘Ž=6, 𝑏=2
  • Eπ‘Ž=2, 𝑏=2

This lesson includes 45 additional question variations for subscribers.

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