Lesson Worksheet: Projectile Motion Mathematics

In this worksheet, we will practice analyzing the motion of a projectile and finding the parametric equations of motion and the Cartesian equation of its path.

Q1:

A particle projected with a velocity (𝑒+𝑒)ij m/s from a fixed point 𝑂 in a horizontal plane landed at a point in the same plane 360 m away. Find the value of 𝑒 and the projectile’s path’s greatest height β„Ž. Take 𝑔=9.8/ms.

  • A𝑒=42, β„Ž=180m
  • B𝑒=59.4, β„Ž=360m
  • C𝑒=42, β„Ž=90m
  • D𝑒=59.4, β„Ž=180m
  • E𝑒=84, β„Ž=360m

Q2:

A particle projected from the origin 𝑂 passed horizontally through a point with a position vector of (10+10)ij m, where i and j are horizontal and vertical unit vectors respectively. Determine the velocity with which the particle left 𝑂, considering the acceleration due to gravity to be 9.8 m/s2.

  • A(14+28)ij m/s
  • B(7+14)ij m/s
  • C(7+28)ij m/s
  • D(14+14)ij m/s
  • E(14+7)ij m/s

Q3:

A particle started moving from 𝑂 with a velocity of (2+15)ij m/s, where i and j are unit vectors horizontally and vertically upward respectively. Find, giving your answer to the nearest integer, the distance of the particle from 𝑂 after 1 s. Consider the acceleration due to gravity to be 9.8 m/s2.

Q4:

If a particle was projected from the origin 𝑂 on a horizontal ground with initial velocity (17+11)ij m/s, write its position vector at time 𝑑 seconds. Consider the acceleration due to gravity to be 9.8 m/s2.

  • A17π‘‘βˆ’ο€Ή11𝑑+4.9𝑑ij m
  • B17𝑑+ο€Ή11π‘‘βˆ’9.8𝑑ij m
  • C17𝑑+ο€Ή11𝑑+9.8𝑑ij m
  • D17π‘‘βˆ’ο€Ή11𝑑+9.8𝑑ij m
  • E17𝑑+ο€Ή11π‘‘βˆ’4.9𝑑ij m

Q5:

A particle was projected from a point 𝑃 with a position vector (17+9)ij m relative to the origin 𝑂. After 2 seconds, it was at a point (32+50)ij m relative to 𝑂, where i and j are the horizontal and vertical unit vectors respectively. Calculate the distance of the particle from 𝑃 after a further 5 seconds. Take the acceleration due to gravity to be 9.8 m/s2.

Q6:

A man in a balcony threw a ball to his friend, who was standing in the street, horizontally with a speed of 6 m/s. Taking the acceleration due to gravity 9.8 m/s2, find the horizontal and vertical components, v and v, of the ball’s velocity 1 second after it was thrown.

  • Av=6/ms and v=6/ms
  • Bv=6/ms and v=9.8/ms
  • Cv=6/ms and v=4.9/ms
  • Dv=6/ms and v=βˆ’4.9/ms
  • Ev=6/ms and v=βˆ’9.8/ms

Q7:

A rock was thrown with a speed of 47 m/s at an angle of elevation 50∘, while a second rock was thrown at an angle of elevation 55∘. If both rocks traveled the same horizontal distance, find, to the nearest two decimal places, the speed with which the second rock was thrown. Take 𝑔=9.8/ms.

Q8:

Find, to one decimal place, a projectile’s speed 3 seconds after it was thrown, given that it flew a total horizontal distance of 282 m for 5 seconds before hitting the ground. Take 𝑔=9.8/ms.

Q9:

Suppose a particle is projected at a speed of 21 m/s and an angle of elevation 51∘. How long will it take for the particle to reach its greatest height? Give your answer correct to two decimal places. Take 𝑔=9.8/ms.

Q10:

As part of a stunt, an aircraft flew up into the sky and then had its engine turned off for a short time. During that time, it was subject to gravitational acceleration of 9.8 m/s2. While the engine was off, the trajectory of the aircraft followed the equation 𝑦=1.77π‘₯βˆ’ο€Ή9.7Γ—10π‘₯οŠͺ. The π‘₯-axis represents horizontal distance, the 𝑦-axis represents vertical distance, and both axes have units in meters. The origin is the point at which the engine was turned off. Find the time taken, in seconds correct to one decimal place, for the aircraft to return to the same height it was at when the engine was turned off.

This lesson includes 59 additional questions and 598 additional question variations for subscribers.

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