Answer:
a) Sketch in annex
b) angle is 22 °
c) grade of the hill is tan 22° = 0,40
Step-by-step explanation: See Annex for free body diagram
According to Newton´s second law
∑ Fy = 0 ⇒ mg cos ∠CAB - Fn = 0
Notice ∠ CAB = ∠ POD ( They have perpendicular sides )
mg = 500 Kg * 9.8 m/sec² ⇒ mg = 4900 [N]
mg cos ∠CAB - Fn = 0 ⇒ 4900*cos ∠CAB = Fn (1)
∑ Fx = ma
mg* sin ∠CAB - Fr = 500* 0.04 m/sec² = 20 [N]
4900 * sin ∠CAB = 1800 + 20 [N]
sin ∠CAB = 1820 / 4900 ⇒ sin ∠CAB = 0.3714
From tables we get
∠CAB = 22°
1/6. since one can't be divided by six into a whole #, it doesn't reduce.
let x = miles
we have x miles/ 60mph plus x miles / 40 mph = 1 hour
x/60 + x/40 = 1
we need to calculate 2x for the round trip
calculate common denominator and rewrite the 2 fractions:
2x/120 + 3x/120 = 1
5x= 120
x = 120/5 = 24 miles
24*2 = 48 miles total
check:
1 way would be 48/2 = 24 miles
24/60 = 0.4 hours to drive 24 miles at 60 mph
24/40 = 0.6 hours to drive 24 miles at 40 mph
0.6 +0.4 = 1 hour
Answer:
b2-4ac , ans is negative . Should have no real roots .
