Sponge - A golf ball rebounds from the floor and travels straight upward with an initial speed of 5.0 m/s. To what maximum height does the ball rise?

In curved motion, displacement is still the straight line from the starting point to the final location. This displacement might not be representative of the actual direction of velocity during the motion of the object.

Instantaneous velocity and instantaneous acceleration can be found for an object by finding the components of the instantaneous vector.

In these situations of two-dimensional motion the x part of the motion occurs exactly as it would if the y part did not exist at all, and vice versa.

Ex. 1 - In the x direction, a spacecraft has an initial velocity component of v0x = +22 m/s and an acceleration component of ax = +24 m/s2. In the y direction, v0y = +14 m/s and ay = +12 m/s2. Right and upward are positive. After a time of 7.0 s, find (a) x and vx, (b) y and vy, and (c) the final velocity of the spacecraft.

In projectile motion, the vx is constant (vx = v0x), ax = 0 In projectile motion, the vx is constant (vx = v0x), ax = 0. But vy changes because of the acceleration due to gravity; ay = 9.80 m/s2 usually.

Ex. 2 - An airplane flies horizontally with a constant velocity of +115 m/s at an altitude of 1050 m. The plane releases a “care package” that falls to the ground along a curved trajectory. Ignoring air resistance, determine the time required for the package to hit the ground.

Ex. 3 - Find the velocity of the package just before it hits the ground.

Ex. 5 - A placekicker kicks a football at an angle of θ = 40 Ex. 5 - A placekicker kicks a football at an angle of θ = 40.0° above the horizontal axis. The initial speed of the ball is v0 = 22 m/s. Find the maximum height H that the ball attains.

Ex. 6 - Determine the time of flight of the football between kickoff and landing.

Ex. 7 - Calculate the range R of the kickoff.

Ex. 8 - A baseball player hits a home run, and the ball lands in the left-field seats, 7.5 m above the point at which the ball was hit. The ball lands with a velocity of 36 m/s at an angle of 28° below the horizontal . Find the initial velocity with which the ball leaves the bat.