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A projectile is fired from a height of 80 M above sea level, horizontally with a speed of 360 M / S, calculate: The time it takes for the projectile to reach the water. The Horizontal scope. The height that remains to descend after 2 seconds of being launched.

User Juanetta
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Answer:

(a) The projectile takes approximately 4.420 seconds to reach the water, (b) The horizontal scope of the projectile is 1591.2 meters, (c) The remaining height to descend after 2 seconds of being launched is 63.624 meters.

Step-by-step explanation:

The projectile experiments a parabolic motion, where horizontal speed remains constant and accelerates vertically due to the gravity effect. Let consider that drag can be neglected, so that kinematic equation are described below:


x = x_(o)+v_(o,x) \cdot t


y = y_(o) + v_(o,y)\cdot t +(1)/(2)\cdot g \cdot t^(2)

Where:


x_(o),
y_(o) - Initial horizontal and vertical position of the projectile, measured in meters.


v_(o,x),
v_(o,y) - Initial horizontal and vertical speed of the projectile, measured in meters per second.


t - Time, measured in seconds.


g - Gravitational acceleration, measured in meters per square second.


x,
y - Current horizontal and vertical position of the projectile, measured in meters.

Given that
x_(o) = 0\,m,
y_(o) = 80\,m,
v_(o,x) = 360\,(m)/(s),
v_(o,y) = 0\,(m)/(s) and
g = -9.807\,(m)/(s^(2)), the kinematic equations are, respectively:


x = 360\cdot t


y = 80-4.094\cdot t^(2)

(a) If
y = 0\,m, the time taken for the projectile to reach the water is:


80 - 4.094\cdot t^(2) = 0


t = \sqrt{(80)/(4.094) }\,s


t \approx 4.420\,s

The projectile takes approximately 4.420 seconds to reach the water.

(b) The horizontal scope is the horizontal distance done by the projectile before reaching the water. If
t \approx 4.420\,s, the horizontal scope of the projectile is:


x = 360\cdot (4.420)


x = 1591.2\,m

The horizontal scope of the projectile is 1591.2 meters.

(c) If
t = 2\,s, the height that remains to descend is:


y = 80-4.094\cdot (2)^(2)


y = 63.624\,m

The remaining height to descend after 2 seconds of being launched is 63.624 meters.

User Selamawit
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