Check Your Understanding A ball is thrown from a window 10.0 m above the ground with an initial horizontal velocity of 3.0 m/s. a) How long will it take the ball to reach the ground? b) How far will the ball travel horizontally (i.e. its range)? Check Your Understanding A rubber duck is launched horizontally from the roof of a 32 m tall building at a velocity of 8.6 m/s. a) What is the duck's time of flight? b) What is the duck's range? Check Your Understanding A child travels down a slide, leaving it with a velocity of 4.2 m's horizontally. The child then experiences projectile motion, landing in a swimming pool 3.2 m below the slide. a) For how long is the child airborne?Check Your Understanding a) For how long is the child airborne? [answer: 0.81 s] b) Determine the child's horizontal displacement while in the air. Check Your Understanding a) For how long is the child airborne? [answer: 0.81 s] b) Determine the child's horizontal displacement while in the air. [answer: 3.4 m [fwd] c) Determine the child's velocity upon entering the water. Projectiles with upward vi An upward v, means that the projectile's initial path is at an angle above the horizontal and DOES NOT equal zero Projectiles travel with a parabolic trajectory because the downward force of gravity accelerates them Analyzing More Complex Projectile Motion The same kinematics equations can be used to analyze problems where the initial velocity is at some angle to the horizontal, Vi = 0 Often, you need to break these problems into different sections to take into account the upward then downward motion You will also need to use vectors components to find the velocity values in the x and y directions Example - draw the example givenCheck Your Understanding A golfer is trying to improve the range of her shot. To do so she drives a golf ball from the top of a steep cliff, 30.0 m above the ground where the ball will land. If the ball has an initial velocity of 25 m/'s and is launched at an angle of 50 above the horizontal, determine the ball's a) time of flight. Check Your Understanding a) time of flight. [answer: 5.1 s] b) its range. Check Your Understanding a) time of flight. [answer: 5.1 s] b) its range. [answer: $2 m [fwd]] c) its final velocity just before it hits the ground.Check Your Understanding A princess, trapped in a castle wraps a message around a rock and throws it from the top of the castle wall with an initial velocity of 12 m/s [420 above the horizontal]. The rock lands just on the far side of the castle's moat, at a level 9.5 m below the initial level. Determine the a) time of flight. Check Your Understanding a) time of flight. [answer: 2.4 s] b) width of the moat. Check Your Understanding time of flight. [answer: 2.4 s] b) width of the moat. [answer: 22 m] c) velocity at impact.Check Your Understanding A superhero launches himself from the top of a building with a velocity of 13 ms at an angle of 25 above the horizontal. If the building is 1? In high a) how far \"'lll he travel horizontally before reaching the ground? h) what is his final velocity