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Vertical Launch Physics
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Let’s use kinematics to analyze an object that has been launched straight up moving 29.4 m/s
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Velocity The object will lose 9.8 m/s of velocity every second because of gravity. (We can refer to them as “gravity bites.”)
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Position Use kinematics equation 2 to calculate the position of the object at any time. ∆ x = ½ at2 + v0t
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9.8 – 9.8 v3 = x3 = 0 m/s 44.1 m ∆ x = ½ at2 + v0t = ½ (-9.8)(3) (3) v2 = x2 = v1 = x1 = v0 = x0 = 9.8 m/s 39.2 m 19.6 m/s 24.5 m 29.4 m/s 0 m v4 = x4 = v5 = x5 = v6 = x6 = -9.8 m/s 39.2 m -19.6 m/s 24.5 m -29.4 m/s 0 m 0 – 9.8 19.6 – 9.8 ∆ x = ½ at2 + v0t = ½ (-9.8)(2) (2) ∆ x = ½ at2 + v0t = ½ (-9.8)(4) (4) -9.8 – 9.8 29.4 – 9.8 ∆ x = ½ at2 + v0t = ½ (-9.8)(1) (1) ∆ x = ½ at2 + v0t = ½ (-9.8)(5) (5) -19.6 – 9.8 ∆ x = ½ at2 + v0t = ½ (-9.8)(6) (6)
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THINGS TO NOTICE: v3 = x3 = 0 m/s 44.1 m v2 = x2 = v1 = x1 = v0 = x0 =
Path is symmetric. Time Up = Time Down Launch speed = impact speed The velocity at he highest point = 0 BUT the acceleration is still m/s2 (turning counts as acceleration). The position is always positive BUT velocity up = + and velocity down = - v2 = x2 = v1 = x1 = v0 = x0 = 9.8 m/s 39.2 m 19.6 m/s 24.5 m 29.4 m/s 0 m v4 = x4 = v5 = x5 = v6 = x6 = -9.8 m/s 39.2 m -19.6 m/s 24.5 m -29.4 m/s 0 m
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Symbolic Alphabet Soup
Solving for Time END: ∆x = v0 = v = a = t = 0 m launch - launch - 9.8 m/s2 ttotal Solving for Height TOP: ∆x = v0 = v = a = t = h launch 0 m/s - 9.8 m/s2 tup = ½ of ttotal Use to find ttotal at the END Use to find height at the TOP
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NUMERIC EXAMPLE A soccer ball is kicked straight up moving 15 m/s. How high will it go? How much air time will it have? END: ∆x = v0 = v = a = t = 0m 15 m/s - 15 m/s - 9.8 m/s2 want TOP: ∆x = v0 = v = a = t = want 15 m/s 0 m/s -9.8 m/s2 ½ (ttotal) = ½ (3.06) = 1.53 s Use 3rd Equation: ∆x = ½ (v0 +v) t Plug in and solve: ∆x = ½ (15 +0) (1.53) = 11.5 m Use 1st Equation: v = at + v0 Solve for t: t = v – v0 a = -15 – 15 -9.8 = 3.06 s
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PRACTICE What launch speed is needed to keep a tennis ball in the air for 3.4 seconds if it is hit straight up?
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PRACTICE How long will an arrow stay in the air if it is fired straight up going 52 m/s?
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PRACTICE How high up will a jumper go if they leave the ground moving 6.4 m/s?
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PRACTICE Bob is trying to throw his backpack over a tall fence. If the fence is 7 meters tall, then how much time will the backpack be in the air?
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PRACTICE How much launch velocity is needed in order for gymnast to jump 1.2 meters while doing a back flip?
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PRACTICE A rocket is launched in the soccer field. After 8 seconds, the rocket crashes back into the grass. How high did the rocket go?
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