Answer:
The x component of this vector is (-1î) unit
Explanation:
Vector position of point 1 = x₁ = 5 (cos (-π/3)î + sin (-π/3)j) = (2.5î - 4.33j)
Vector position of point 2 = x₂ =3(cos 60°î + sin 60°j) = (1.5î + 2.598j)
Vector joining the two point, x₁₂ = x₂ - x₁ = (1.5î + 2.598j) - (2.5î - 4.33j) = - 1.0 î + 6.928j
The x component of this vector is -1î unit.
Linear momentum (mass x speed) has to be conserved.
-- Momentum before the jump:
(boy's mass) x (boy's speed) = (25 kg) x (4.0 m/s) = 100 kg-m/s
(cart's mass) x (cart's speed) = (15 kg) x (zero) = zero
Total momentum before the jump: (100 kg-m/s) + (zero) = (100 kg-m/s)
-- Momentum after the jump:
(mass of boy+cart) x (speed of boy+cart) = (40 kg) x (speed)
-- Momentum after the jump = momentum before the jump
(40 kg) x (speed) = 100 kg-m/s
Divide each side by 40 kg:
Speed = (100 kg-m/s) / (40 kg)
<em>Speed = 2.5 m/s</em> (d)
The formula for GPE is GPE=mgh. M is for mass, G is for acceleration due to gravity (9.8 m/s/s) and H is for the height.
GPE= mgh
GPE= 500 (kg)*9.8 (m/s/s)* 10 (feet)
GPE= 49,000