Answer:
a) x = 40 t
, y = 39 t
, z = 6 + 32 t - 16 t
², b) x = 80 feet
, y = 78 feet
, the ball came into the field
Explanation:
a) This is a projectile launch exercise, where in the x and y axes there is no acceleration and in the z axis the acceleration of the acceleration of gravity, let's write the equations of motion in each axis
Since the cast is in the center of the field, let's place the coordinate system
x₀ = 0
y₀ = 0
z₀ = 6 feet
x-axis (towards end zone, GOAL zone)
x = xo + v₀ₓ t
x = 40 t
y-axis (field width)
y = y₀ + 
t
y = 39 t
z axis (vertical)
z = z₀ + v_{oz} t - ½ g t²
z = 6 + 32 t - ½ 32 t²
z = 6 + 32 t - 16 t
²
b) The player catches the ball at the same height as it came out, so we can find the time it takes to arrive
z = 6
6 = 6 + 32 t - 16 t²
(t - 2)t = 0
t=0 s
t= 2 s
The ball position
x = 40 2
x = 80 feet
y = 39 2
y = 78 feet
the dimensions of the field from the coordinate system (center of the field) are
x_total = 150 feet
y _total = 80 feet
so we can see that the ball came into the field
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I hope this helps! :)
Answer:
The answer is in 3 point
Choose which point you like
5.972 × 10^24 kg
it is the weight of earth
hope it is helpful to you
Answer:
a) 
b) 
Explanation:
Given:
- upward acceleration of the helicopter,
- time after the takeoff after which the engine is shut off,
a)
<u>Maximum height reached by the helicopter:</u>
using the equation of motion,
where:
u = initial velocity of the helicopter = 0 (took-off from ground)
t = time of observation
b)
- time after which Austin Powers deploys parachute(time of free fall),
- acceleration after deploying the parachute,
<u>height fallen freely by Austin:</u>
where:
initial velocity of fall at the top = 0 (begins from the max height where the system is momentarily at rest)
time of free fall
<u>Velocity just before opening the parachute:</u>
<u>Time taken by the helicopter to fall:</u>
where:
initial velocity of the helicopter just before it begins falling freely = 0
time taken by the helicopter to fall on ground
height from where it falls = 250 m
now,
From the above time 7 seconds are taken for free fall and the remaining time to fall with parachute.
<u>remaining time,</u>
<u>Now the height fallen in the remaining time using parachute:</u>
<u>Now the height of Austin above the ground when the helicopter crashed on the ground:</u>
