Practice: You throw a rock off the top of a tall building at an upward angle of 15°. At t=3 s, the rock’s horizontal displacement from you is 52m. How high does the rock get above the top of the building?

Concept #1: Solving Non-Symmetrical Upward Launch Problems

Practice: You throw a rock off the top of a tall building at an upward angle of 15°. At t=3 s, the rock’s horizontal displacement from you is 52m. How high does the rock get above the top of the building?

Example #1: A child throws a ball from ground level with an initial speed of 13 m/s at an upward angle of 67.4°. It reaches its maximum height directly above the edge of a roof, then lands on the roof, 3 m from the edge. How high is the roof?

Example #2: A catapult launches a stone with an initial velocity of 50 m/s at an angle of 56° above the horizontal. What is the direction of the stone's velocity when it hits a castle wall 6 seconds later?

Concept #2: Using Single Intervals in Positive Launch Problems

Practice: A ball is thrown from the top of a 50-m-tall building with a speed of 40 m/s at an angle of 37° above the horizontal. How far horizontally does the ball travel before hitting the ground?