Horizontally Launched Projectiles A ball rolling off the table is an excellent example of an object thrown into the air with horizontal initial velocity (velocity at the time when the object is launched). The ball becomes airborne when leaving the table. If the ball rolls along the table with constant horizontal velocity, then the moment it leaves the table, it has the same horizontal velocity with which it rolled along the table and zero vertical velocity.
The ball would continue its motion with the same speed and direction unless there is an acceleration. In the horizontal direction, there are no forces on the motion which means that nothing can give the object horizontal acceleration. Horizontal velocity remains CONSTANT, because we neglect air resistance in our calculations, and the ball covers equal distances in equal intervals of time. In vertical direction there is gravitational acceleration. The projectile accelerates downward. When these two motions are combined - vertical free fall motion and uniform horizontal motion - the trajectory will be a parabola. click me
Projectiles Launched at an Angle v q vx Often, the projectiles are launched at an angle. To solve the problem, we resolve this initial velocity into its horizontal and vertical components. vy • Horizontal component vxis constant throughout the motion. Vertical component vy is decreasing on the way up, becoming zero at the top, and increasing on the way down. click me Horizontal component of motion for a projectile is completely independent of the vertical component of the motion. Their combined effects produce the variety of curved paths - parabolas that projectile follow.
Zookeeper who found the special way to feed monkey banana. If there was no gravity acting on either the banana or the monkey, banana moves in a straight line and the monkey does not fall once he lets go of the tree. As such, a banana aimed directly at the monkey will hit the monkey. The zookeeper aims at the monkey and shoots the banana very fast . The banana reaches the monkey before the monkey has fallen very far. The zookeeper aims above the monkey’s head.The banana misses the monkey, moving over his head. banana passes as far above the monkey's head as it was originally aimed. The zookeeper aims at the monkey and shoots the banana with a slow speed . Banana hits the monkey after the monkey has fallen considerably far.
In conclusion, the key to the zookeeper's dilemma is to aim directly at the monkey. Both banana and monkey experience the same acceleration since gravity causes all objects to accelerate at the same rate regardless of their mass. Since both banana and monkey experience the same acceleration each will fall equal amounts.
When an object is launched at an angle, it has an initial velocity that can be resolved into horizontal and vertical components. The horizontal component of initial velocity IS CONSTANT (i.e. has no acceleration) because there are no forces acting upon it. The vertical component of initial velocity changes because it experiences downward acceleration due to the force of gravity. Remind your self continuously: forces are not required for an object to be moving; once in motion, the presence of forces will only serve to accelerate such objects.
Check Your Understanding -- The Truck and The Ball Imagine a pickup truck moving with a constant speed along a city street. In the course of its motion, a ball is projected straight upwards by a launcher located in the bed of the truck. Imagine as well that the ball does not encounter a significant amount of air resistance. Where will the ball land? In front of the truck, 2) In the truck, 3) Behind the truck, 4) We need to know the velocity of th e truck and ball to answer How do you know?
750 600 450 ACTUAL PATH 300 150 IDEAL PATH Range of Projectile Motion (when starting and ending height are equal) R = 2 vi2 sinθ cos θ the same range is obtained for two projection angles that add up to 900 Projectile thrown with the same speed at 300 and 600 will have the same range. The one at 300 remains in the air for a shorter time. This is our only new equation! What if we have air resistance? Air resistance shortens the range of the object, and the path is no longer a parabola. You won’t need to mathematically solve this, but you DO need to be able to describe how air resistance affects the motion.
Check your understanding • If a projectile launches and lands at the same height, what affects how far it travels? Initial speed and angle • What affects how long a projectile stays in the air? Height of launch relative to landing, and the vertical component of initial velocity.
Check your understanding • How does a projectile’s vertical velocity change over time? It becomes more negative. • How does a projectile’s horizontal velocity change over time? It doesn’t change (if air resistance is ignored) • How does a projectile’s acceleration change over time? It doesn’t change (always 9.81 m/s2 down)
Closure Exit Ticket Homework
Solving Projectile Motion Problems To solve projectile motion problems, you must separate the horizontal and vertical components of motion. • Resolve the launch velocity to find the vix and viy. (Use SOH CAH TOA) • Divide your paper into two sections – one for horizontal and one for vertical • Write the relevant equations and known variables in the appropriate sections • Recognize that horizontal and vertical sides are linked by time in the air. You may use time to find other variables on either section.