Answer:
3.6 m
Explanation:
let x = horizontal distance between emily and allison should be for allison to catch the ball
Find horizontal speed of the ball
vx = 12 sin 30 = 12 x 0.5 = 6 m/s
To find time taken, we will use vertical values of the ball motion
Initial velocity in vertical direction
u = 12 cos 30 = 10.392 m/s
let a = g = 9.8m/s2
Use equation of motion
s = ut +1/2at^2
s = vertical distance = 8
8 = (10.392)t + (1/2)(9.8)t^2
8 = (10.392)t + (4.9)t^2
4.9t^2 + 10.392t - 8 = 0
Using formula of quadratic or calculator, we'll find
t = 0.6 and t = -2.72
We pick t=0.6s since it's not logical time in negative
Assuming no air resistance or external forces, the ball will move 6m/s horizontally. Hence using the formula of speed
speed vx = distance x / time
x = (vx)(t)
= 6 x 0.6
= 3.6 m
Answer:
n = 2.06 moles
Explanation:
The absolute pressure at depth of 27 inches can be calculated by:
Pressure = Pressure read + Zero Gauge pressure
Zero Gauge pressure = 14.7 psi
Pressure read = 480 psi
Total pressure = 480 psi + 14.7 psi = 494.7 psi
P (psi) = 1/14.696 P(atm)
So, Pressure = 33.66 atm
Temperature = 25°C
The conversion of T( °C) to T(K) is shown below:
T(K) = T( °C) + 273.15
So,
T = (25 + 273.15) K = 298.15 K
T = 298.15 K
Volume = 1.50 L
Using ideal gas equation as:
PV=nRT
where,
P is the pressure
V is the volume
n is the number of moles
T is the temperature
R is Gas constant having value = 0.0821 L.atm/K.mol
Applying the equation as:
33.66 atm × 1.50 L = n × 0.0821 L.atm/K.mol × 298.15 K
⇒n = 2.06 moles
Answer:
a) The maximum possible acceleration the truck can give the SUV is 7.5 meters per second squared
b) The force of the SUV's bumper on the truck's bumper is 18000 newtons
Explanation:
a) By Newton's second law we can find the relation between force and acceleration of the SUV:
With F the maximum force the truck applies to the SUV, m the mass of the SUV and a the acceleration of the SUV; solving for a:
b) Because at this acceleration the truck's bumper makes a force of 18000 N on the SUV’s bumper by Third Newton’s law the force of the SUV’s bumper on the truck’s bumper is 18000 N too because they are action-reaction force pairs.
Answer:
B= 
≅8.06
Explanation:
Using the Pythagorean theorem:
= 
+ 
where C represents the length of the hypotenuse and A and B the lengths of the triangle's other two sides, we can find out the lenght of B assuming the value of the hypotenuse being 9 and A being 4.
=
+
81= 16+
81-16=
B= ≅8.06
