Answer:
1.1648×10⁻¹¹ N
Explanation:
Using
F = qvBsinФ..................... Equation 1
Where F = Force on the proton, q = charge, v = velocity, B = magnetic Field, Ф = angle between the magnetic Field and the velocity.
Note: The angle between v and B = 90°
Given: v = 5.2×10⁷ m/s, B = 1.4 T, q = 1.6×10⁻¹⁹ C, Ф = 90°
Substitute into equation 1
F = 1.6×10⁻¹⁹(5.2×10⁷)(1.4)sin90°
F = 11.648×10⁻¹²
F = 1.1648×10⁻¹¹ N.
(1)
Cheetah speed: 
Its position at time t is given by
(1)
Gazelle speed: 
the gazelle starts S0=96.8 m ahead, therefore its position at time t is given by
(2)
The cheetah reaches the gazelle when
. Therefore, equalizing (1) and (2) and solving for t, we find the time the cheetah needs to catch the gazelle:



(2) To solve the problem, we have to calculate the distance that the two animals can cover in t=7.5 s.
Cheetah: 
Gazelle: 
So, the gazelle should be ahead of the cheetah of at least




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If west means the west of the axis x the velocity equal :

Answer:
a) v = √(v₀² + 2g h), b) Δt = 2 v₀ / g
Explanation:
For this exercise we will use the mathematical expressions, where the directional towards at is considered positive.
The velocity of each ball is
ball 1. thrown upwards vo is positive
v² = v₀² - 2 g (y-y₀)
in this case the height y is zero and the height i = h
v = √(v₀² + 2g h)
ball 2 thrown down, in this case vo is negative
v = √(v₀² + 2g h)
The times to get to the ground
ball 1
v = v₀ - g t₁
t₁ =
ball 2
v = -v₀ - g t₂
t₂ = - \frac{v_{o} + v }{ g}
From the previous part, we saw that the speeds of the two balls are the same when reaching the ground, so the time difference is
Δt = t₂ -t₁
Δt =
Δt = 2 v₀ / g