A car slows from 14 m/s to 5 m/s along a stretch of track. The report gives no times at all. Which kinematic equation can work with exactly the numbers given?
A ball leaves a thrower's hand moving straight up at 21 m/s. How high does it rise? The question gives no time and asks for none.
You've already seen the kinematic equation with no time in it: v² = v₀² + 2aΔx. At the top of the rise the velocity is zero for an instant, and the acceleration is still 9.8 m/s² downward. That v = 0 pins down the height.
Take up as positive: v₀ is the launch velocity and a = −9.8 m/s². Make Δx the subject, the same rearrangement you've already used: Δx = (v² − v₀²)/(2a).
A ball is thrown straight up at 21 m/s. Air resistance is ignored. How high above the launch point does it rise?
Write down the values in the question:
v = 0 (at the highest point)
v₀ = 21 m/s
a = −9.8 m/s² (taking up as positive)
Write down the equation:
v² = v₀² + 2aΔx
Make Δx the subject:
Δx = (v² − v₀²)/(2a)
Substitute in the values:
Δx = (0 − 21²)/(2 × (−9.8))
Simplify:
Δx = −441 / −19.6 = 22.5 m above the launch point
Substituting v = 0 and a = −9.8 m/s² always gives Δx = (0 − v₀²)/(−19.6). The two negative signs cancel, so the height comes out positive: the top is above the launch point.
A ball is thrown straight up at 28 m/s. Air resistance is ignored. How high above the launch point does it rise? Enter the height in meters.
A softball is hit straight up at 29.4 m/s. Air resistance is ignored. What is its maximum height above the bat?
Write down the values in the question:
v = 0 (at the highest point)
v₀ = 29.4 m/s
a = −9.8 m/s² (taking up as positive)
Write down the equation:
v² = v₀² + 2aΔx
Make Δx the subject:
Δx = (v² − v₀²)/(2a)
Substitute in the values:
Δx = (0 − 29.4²)/(2 × (−9.8))
Simplify:
Δx = −864.36 / −19.6 = 44.1 m above the bat
A cork pops straight up out of a bottle at 9.8 m/s. Air resistance is ignored. How high above the bottle does the cork rise? Enter the height in meters.
A stunt ball is fired straight up from a ground-level launcher at 35 m/s. Air resistance is ignored. What is its maximum height above the launcher? Enter the height in meters.
A baseball leaves a throwing machine pointed straight up at 42 m/s. Air resistance is ignored. How high above the machine does the ball rise? Enter the height in meters.
A juggler tosses a ring straight up at 24.5 m/s. Air resistance is ignored. How far above the release point is the ring when it is momentarily at rest? Enter the height in meters.
A model rocket's motor burns out while the rocket is coasting straight up at 49 m/s. From burnout it is in free fall, with air resistance ignored. How much higher does it rise after burnout? Enter the height in meters.