Projectile

Projectiles

POSTED IN PHYSICS, MECHANICS

Contents

• Resolving the horizontal and vertical components
• Solving projectile questions
  • Worked examples

Projectiles are composed of two components: a vertical component and a horizontal component. Assuming there is no air resistance or friction the vertical acceleration is constant (9.81ms^-1, due to gravity) and the horizontal velocity is constant. The horizontal and vertical components act independently; they have no effect on one another.

Resolving the horizontal and vertical components

Resolving the horizontal and vertical components of a projectile is covered in full in the vectors topic. To recap:

• The horizontal component, A_x = A cos
• The vertical component, A_y = A sin

Solving projectile questions

Projectiles are solved using the kinematic equations. Projectile questions however require some thought, it's not usually as simple as plugging in some values into an equation, because of this they are a favourite in exams. A few things that you need to realise about projectiles to help answer questions:

• At the peak height of a projectile the velocity is 0
• The range of a projectile that travels in a parabola (such as a golf ball being hit) is twice the distance it takes to reach it's peak height
• A projectile will decelerate from its initial velocity to 0ms at it's peak with an acceleration of -9.81ms^-2 before accelerating at +9.81ms^-2 from 0 to it's final velocity
• The trajectory (angle relative to the horizontal displacement) of a projectile can be calculated using trigonometry as 

Worked examples

Example question: An angry teenager throws out his computer from his bedroom window at 4ms^-1, it lands on the road outside 2 seconds later. Find: (a) the height of the window (b) out far from the window it hits the ground

Worked answer (a) As with any question concerning the kinematic equations it's best to start out by listing what variables you know and what ones you want to know. In this case we want the displacement, s and we have been given the value t in the question. We are expected to realise that the downwards acceleration is 9.81ms^-2 and the initial vertical velocity is 0. Using the equation  we can find s:




(b) requires less work. The computer was ejected out of the window at a speed of 2ms^-1 and travelled for 2 seconds, therefore the distance travelled along the horizontal is 4 metres.

Example question: A golf ball is hit at an angle of 30 degrees to the horizontal at a speed of 10ms^-1, how far does it travel?

Worked answer: For a lot of projectile questions drawing a diagram is the best way to start:



The next step is to calculate the initial horizontal and vertical components:




The range of the projectile is given by the time spent in the air and the horizontal component. As we haven't been given the time it needs to be calculated. As just calculated, the projectile is has an initial vertical velocity of 5ms^-1 (u) and will decelerate at -9.81ms^-1 (a) to 0 (v). Therefore the time taken is given by the equation :



The initial horizontal velocity will remain constant and so the range is 8.66 (A_x) x 0.5096 (t) which is around 4.4 metres.