Answer:
Explanation:
The formula for Kinetic Energy is
. Filling in:
It looks like we only need 1 significant digit here but I'll give you 2 and you can round how you want.
KE = 2.4 × 10⁵ J
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
Answer: 0.5N
Explanation:
Gravitational force is calculated using the formula :
F = Gm1m2/r^2
Where G is the gravitational constant (6.67 × 10^-11)
At a distance 'r' of 2metres apart:
Mass of objects are m1 and m2
Gravitational force 'F1' = 2N
Inputting values into the formula :
2 = Gm1m2 / 2^2 - - - - - (1)
At a distance 'r' of 4meters apart:
Mass of objects are m1 and m2
Gravitational force 'F2' = y
Inputting values
F2 = Gm1m2 / 4^2 - - - - - (2)
Dividing equations 1 and 2
2 = Gm1m2 / 2^2 ÷ F2 = Gm1m2 / 4^2
2 / F2 = (Gm1m2 / 4) / (Gm1m2 / 16)
2 / F2 = (Gm1m2 / 4) × (16 / Gm1m2)
2/F2 = 16 / 4
Cross multiply
2 × 4 = 16 × F2
8 = 16F2
F2 = 8/16
F2 = 0.5N
Answer:
a) t=1s
y = 10.1m
v=5.2m/s
b) t=1.5s
y =11.475 m
v=0.3m/s
c) t=2s
y =10.4 m
v=-4.6m/s (The minus sign (-) indicates that the ball is already going down)
Explanation:
Conceptual analysis
We apply the free fall formula for position (y) and speed (v) at any time (t).
As gravity opposes movement the sign in the equations is negative.:
y = vi*t - ½ g*t2 Equation 1
v=vit-g*t Equation 2
y: The vertical distance the ball moves at time t
vi: Initial speed
g= acceleration due to gravity
v= Speed the ball moves at time t
Known information
We know the following data:
Vi=15 m / s

t=1s ,1.5s,2s
Development of problem
We replace t in the equations (1) and (2)
a) t=1s
=15-4.9=10.1m
v=15-9.8*1 =15-9.8 =5.2m/s
b) t=1.5s
=22.5-11.025=11.475 m
v=15-9.8*1.5 =15-14.7=0.3m/s
c) t=2s
= 30-19.6=10.4 m
v=15-9.8*2 =15-19.6=-4.6m/s (The minus sign (-) indicates that the ball is already going down)