Ican Flye performs the infamous "Triple Lindy" dive from a point 15 m above water.
a. If he starts his dive with no vertical velocity, how long will it take him to hit the water?
b. How fast will he be traveling vertically when he hits the water?
c. If he hits the water at a point 4 m horizontally out from the takeoff point, what is his horizontal velocity at takeoff and again at the instant he hits the water?
a.
h = (1/2) g t^2
so
4.9 t^2 = 15
find t
b.
v = gt
c.
u is constant. There is no vertical force
u = 4/t
To solve these problems, we can use the principles of projectile motion. Since Ican Flye starts with no vertical velocity (meaning there is no initial upward or downward movement), we can assume the only force acting on him is gravity.
a. To find how long it takes for Ican Flye to hit the water, we can use the kinematic equation:
d = v0 * t + (1/2) * a * t^2
In this equation:
- d is the distance (15m) he falls
- v0 is the initial vertical velocity (0 m/s)
- a is the acceleration due to gravity (-9.8 m/s^2)
- t is the time we want to find
Plugging in the values, we have:
15m = 0 * t + (1/2) * (-9.8m/s^2) * t^2
Simplifying the equation:
0 = -4.9t^2 + 15
Rearranging the equation to solve for t:
4.9t^2 = 15
t^2 = 15 / 4.9
t ≈ √(15 / 4.9)
t ≈ 1.28s
Therefore, it will take approximately 1.28 seconds for Ican Flye to hit the water.
b. To find how fast Ican Flye will be traveling vertically when he hits the water, we can use the equation:
v = v0 + a * t
In this equation:
- v is the final vertical velocity (what we want to find)
- v0 is the initial vertical velocity (0 m/s)
- a is the acceleration due to gravity (-9.8 m/s^2)
- t is the time it takes to hit the water (1.28s)
Plugging in the values, we have:
v = 0 + (-9.8m/s^2) * 1.28s
v ≈ -12.54m/s
Therefore, Ican Flye will be traveling vertically at approximately -12.54 m/s when he hits the water. The negative sign indicates downward direction.
c. To find his horizontal velocity at takeoff and at the instant he hits the water, we need to consider that vertical and horizontal motions are independent of each other.
At takeoff (and therefore throughout the entire motion), there is no horizontal force acting on Ican Flye. Thus, his horizontal velocity remains constant.
Therefore, his horizontal velocity at takeoff and the instant he hits the water will be the same.
Since no values are given for horizontal velocity, we cannot determine the exact speed. However, we can assume it remains constant as there are no horizontal forces acting on Ican Flye during his motion.