Assuming metric units, metre, kilogram and seconds
Best approach: draw a free body diagram and identify forces acting on the child, which are:
gravity, which can be decomposed into normal and parallel (to slide) components
N=mg(cos(theta)) [pressing on slide surface]
F=mg(sin(theta)) [pushing child downwards, also cause for acceleration]
m=mass of child (in kg)
g=acceleration due to gravity = 9.81 m/s^2
theta=angle with horizontal = 42 degrees
Similarly, kinetic friction is slowing down the child, pushing against F, and equal to
Fr=mu*N=mu*mg(cos(theta))
mu=coefficient of kinetic friction = 0.2
The net force pushing child downwards along slide is therefore
Fnet=F-Fr
=mg(sin(theta))-mu*mg(cos(theta))
=mg(sin(theta)-mu*cos(theta)) [ assuming sin(theta)> mu*cos(theta) ]
From Newton's second law,
F=ma, or
a=F/m
=mg(sin(theta)-mu*cos(theta)) / m
= g(sin(theta)-mu*cos(theta)) [ m/s^2]
In case imperial units are used, g is approximately 32.2 feet/s^2.
and the answer will be in the same units [ft/s^2] since sin, cos and mu are pure numbers.
<h3>
sin22° = 5/4</h3><h3>
tan22° = 3/√55</h3>
As we know that , sinA = opposite/hypotenuse & tanA = opposite/adjacent
So here we can find sin22° , because they already given the sides opposite & hypotenuse . And we can't find tann22° because they given the value of opposite but not given the value of adjacent side of the angle 22°
Now finding the adjacent side using
Pythagoras theorem :-
• Hypotenuse² = Base² + Height²
=> 40² = Base² + 15²
=> 1600 - 225 = Base²
=> Base² = 1375
=> Base = √1375
=> Base = 5√55
Now ,
- tan22° = Opposite/Adjacent = 15/5√55 = 3/√55
- sin22° = Opposite/hypotenuse = 15/40 = 5/4
Answer:
<h2>The slope m = -2</h2>
Step-by-step explanation:
The slope-intercept form of the equation of line:
We have
Therefore we have the slope = -2.
Answer:
Step-by-step explanation:
-7x = x² + 12
Set equation to zero:
x² + 7x + 12 = 0
Quadratic formula:
x = [-7±√(7²-4·1·12)]/[2·1]
= [-7±√1]/2
= -3,-4
The zeros are -3 and -4
