The first step is to convert the initial velocity to ft/s. One mile is 5280 feet. One hour is 3600 seconds.
1 mph = 5280 ÷ 3600 = 88/60 = 22/15 This is approximately 1.4667 ft/s. V = 86 * 22/15 = 1892/15 This is approximately 126.133 ft/s. Since the unit of velocity is ft/s, we need to determine the value of g in ft/s^2.
9.81 m/s^2 * 100 cm/m * 1 in/2.54 cm * 1 ft/12 in = 32.18503937 ft/s^2 This is usually rounded to 32.2 ft/s^2. During the 0.510 second, the ball moved from its initial height up to its maximum height and down to its initial height. When the ball is at its maximum height, its vertical velocity is 0 ft/s.
This happens at one half of this time. Let’s use following equation to determine the ball’s initial vertical velocity. Vf = vi – a * t 0 = vi – 32.2 * 0.255 vi = 8.211 ft/s Initial vertical velocity = v * sin?
Initial horizontal velocity = v * cos? Let’s use the following equation to determine this number. (v * sin?)^2 + (v * cos?)^2 = v^2 8.211^2 + (v * cos?)^2 = (1892/15)^2 (v * cos?)^2 = (1892/15)^2 – 8.211^2 v * cos?
=?(1892/15)^2 – 8.211^2) = 125.8657907 ft/s.
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