Projectile Motion

• A projectile is an object upon which the only force acting is gravity.
• An object dropped from rest (or thrown down with an initial velocity) is a projectile (provided that the influence of air resistance is negligible).
• An object that is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible).
• An object which is thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible).
• Projectile motion can be understood by considering motion in one direction: vertically.
• If an object is dropped from rest, then the initial velocity is zero, v_i = 0 m/s.
• The time of flight of a dart can be calculated by the equation t = d/v, where d is the distance the dart travels and v is the velocity of the dart.
• The horizontal motion of a dart is calculated by the equation v = d/t, where d is the distance the dart travels and t is the time of flight.
• The horizontal speed of projection of a dart is calculated by the equation v = at, where a is the acceleration of the dart and t is the time of flight.
• The vertical motion of a dart is calculated by the equation a = v/t, where v is the speed of the dart and t is the time of flight.
• The motion in projectile motion is in the direction of the acceleration, a = g = +9.81 m/s.
• The equation for the motion of a projectile is v_f = v_i + at, where d = (v_i + v_f)t.
• At the maximum height in projectile motion, d_max, the velocity is zero, v = 0 m/s.
• The velocity when the ball has reached the initial position, d = 0, is the same as the initial velocity, v_i.
• A projectile drops beyond the point it was released, provided that the influence of air resistance is negligible.
• The motion in projectile motion is initially in the opposite direction of the acceleration, a = g = -9.81 m/s.
• The time it takes to reach the sea can be calculated.
• If air resistance is ignored the vertical height of the object at given times after the start is the same no matter what horizontal velocity it had at the moment of release.
• The speed of impact of the parcel on the ground can be calculated.
• The height of the aircraft above the ground can be calculated.
• An object is projected horizontally at a speed of 16m/s into the sea from a cliff top of height 45.0m.
• The time to travel all the way up and back to its original height, d = 0m, can be calculated by assuming it was dropped with initial speed the same as the original speed.
• The distance travelled horizontally by the object can be calculated.
• The answer is 4 seconds, calculated by assuming it is being dropped from the top at rest with a new value for d: distance to the top + 20m, and calculating the time.
• At the maximum height, dmax, the velocity, v = 0 m/s.
• The time taken for the object to reach the ground along the parabolic path is the same as if it were dropped vertically.
• The parcel hits the ground 8.5 seconds later.
• The horizontal distance travelled in this time by the parcel and the aircraft can be calculated.
• The parabolic path for an object projected horizontally is shown in the diagram.
• A parcel is released from an aircraft travelling horizontally at a speed of 120m/s above level ground.
• The impact vertical velocity of the object can be calculated.
• The time it takes for a stone to hit the ground 20m below is approximately 4 seconds.
• A projectile is an object upon which the only force acting is gravity.
• An object dropped from rest (or thrown down with an initial velocity) is a projectile (provided that the influence of air resistance is negligible).
• An object that is thrown vertically upward is also a projectile (provided that the influence of air resistance is negligible).
• An object which is thrown upward at an angle to the horizontal is also a projectile (provided that the influence of air resistance is negligible).
• Projectile motion can be understood by considering motion in one direction: vertically.
• If an object is dropped from rest, then the initial velocity is zero, v_i = 0 m/s.
• The time of flight of a dart is calculated by the equation t = d/v, where d is the distance and v is the velocity.
• The vertical motion of a dart is calculated by the equation a = v/t, where v is the acceleration and t is the time of flight.